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185 | Let $f(x) = -4x^{2}-8x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}-8x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = -8, c = 1$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot -4 \cdot 1}}{2 \cdot -4}$ $ x = \dfrac{8 \pm \sqrt{80}}{-8}$ $ x = \dfrac{8 \pm 4\sqrt{5}}{-8}$ $x =\dfrac{2 \pm \sqrt{5}}{-2}$ |
185 | Let $f(x) = -2x^{2}-3x+5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}-3x+5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = -3, c = 5$ $ x = \dfrac{+ 3 \pm \sqrt{(-3)^{2} - 4 \cdot -2 \cdot 5}}{2 \cdot -2}$ $ x = \dfrac{3 \pm \sqrt{49}}{-4}$ $ x = \dfrac{3 \pm 7}{-4}$ $x =-\frac{5}{2},1$ |
185 | Let $f(x) = 10x^{2}-9x-3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $10x^{2}-9x-3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 10, b = -9, c = -3$ $ x = \dfrac{+ 9 \pm \sqrt{(-9)^{2} - 4 \cdot 10 \cdot -3}}{2 \cdot 10}$ $ x = \dfrac{9 \pm \sqrt{201}}{20}$ $ x = \dfrac{9 \pm \sqrt{201}}{20}$ $x =\dfrac{9 \pm \sqrt{201}}{20}$ |
185 | Let $f(x) = -2x^{2}+7x+7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}+7x+7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = 7, c = 7$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot -2 \cdot 7}}{2 \cdot -2}$ $ x = \dfrac{-7 \pm \sqrt{105}}{-4}$ $ x = \dfrac{-7 \pm \sqrt{105}}{-4}$ $x =\dfrac{-7 \pm \sqrt{105}}{-4}$ |
185 | Let $f(x) = -9x^{2}-2x+5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}-2x+5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = -2, c = 5$ $ x = \dfrac{+ 2 \pm \sqrt{(-2)^{2} - 4 \cdot -9 \cdot 5}}{2 \cdot -9}$ $ x = \dfrac{2 \pm \sqrt{184}}{-18}$ $ x = \dfrac{2 \pm 2\sqrt{46}}{-18}$ $x =\dfrac{1 \pm \sqrt{46}}{-9}$ |
185 | Let $f(x) = -8x^{2}-3x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-8x^{2}-3x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -8, b = -3, c = 1$ $ x = \dfrac{+ 3 \pm \sqrt{(-3)^{2} - 4 \cdot -8 \cdot 1}}{2 \cdot -8}$ $ x = \dfrac{3 \pm \sqrt{41}}{-16}$ $ x = \dfrac{3 \pm \sqrt{41}}{-16}$ $x =\dfrac{3 \pm \sqrt{41}}{-16}$ |
185 | Let $f(x) = 5x^{2}-7x-2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $5x^{2}-7x-2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 5, b = -7, c = -2$ $ x = \dfrac{+ 7 \pm \sqrt{(-7)^{2} - 4 \cdot 5 \cdot -2}}{2 \cdot 5}$ $ x = \dfrac{7 \pm \sqrt{89}}{10}$ $ x = \dfrac{7 \pm \sqrt{89}}{10}$ $x =\dfrac{7 \pm \sqrt{89}}{10}$ |
185 | Let $f(x) = -7x^{2}-10x+10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}-10x+10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = -10, c = 10$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot -7 \cdot 10}}{2 \cdot -7}$ $ x = \dfrac{10 \pm \sqrt{380}}{-14}$ $ x = \dfrac{10 \pm 2\sqrt{95}}{-14}$ $x =\dfrac{5 \pm \sqrt{95}}{-7}$ |
185 | Let $f(x) = 7x^{2}-6x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}-6x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = -6, c = 1$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot 7 \cdot 1}}{2 \cdot 7}$ $ x = \dfrac{6 \pm \sqrt{8}}{14}$ $ x = \dfrac{6 \pm 2\sqrt{2}}{14}$ $x =\dfrac{3 \pm \sqrt{2}}{7}$ |
185 | Let $f(x) = 6x^{2}+x-5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}+x-5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = 1, c = -5$ $ x = \dfrac{-1 \pm \sqrt{1^{2} - 4 \cdot 6 \cdot -5}}{2 \cdot 6}$ $ x = \dfrac{-1 \pm \sqrt{121}}{12}$ $ x = \dfrac{-1 \pm 11}{12}$ $x =\frac{5}{6},-1$ |
185 | Let $f(x) = 8x^{2}-6x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $8x^{2}-6x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 8, b = -6, c = -7$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot 8 \cdot -7}}{2 \cdot 8}$ $ x = \dfrac{6 \pm \sqrt{260}}{16}$ $ x = \dfrac{6 \pm 2\sqrt{65}}{16}$ $x =\dfrac{3 \pm \sqrt{65}}{8}$ |
185 | Let $f(x) = 8x^{2}+3x-3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $8x^{2}+3x-3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 8, b = 3, c = -3$ $ x = \dfrac{-3 \pm \sqrt{3^{2} - 4 \cdot 8 \cdot -3}}{2 \cdot 8}$ $ x = \dfrac{-3 \pm \sqrt{105}}{16}$ $ x = \dfrac{-3 \pm \sqrt{105}}{16}$ $x =\dfrac{-3 \pm \sqrt{105}}{16}$ |
185 | Let $f(x) = 7x^{2}+x-8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}+x-8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = 1, c = -8$ $ x = \dfrac{-1 \pm \sqrt{1^{2} - 4 \cdot 7 \cdot -8}}{2 \cdot 7}$ $ x = \dfrac{-1 \pm \sqrt{225}}{14}$ $ x = \dfrac{-1 \pm 15}{14}$ $x =1,-\frac{8}{7}$ |
185 | Let $f(x) = 7x^{2}-10x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}-10x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = -10, c = -6$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot 7 \cdot -6}}{2 \cdot 7}$ $ x = \dfrac{10 \pm \sqrt{268}}{14}$ $ x = \dfrac{10 \pm 2\sqrt{67}}{14}$ $x =\dfrac{5 \pm \sqrt{67}}{7}$ |
185 | Let $f(x) = 9x^{2}-10x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $9x^{2}-10x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 9, b = -10, c = -7$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot 9 \cdot -7}}{2 \cdot 9}$ $ x = \dfrac{10 \pm \sqrt{352}}{18}$ $ x = \dfrac{10 \pm 4\sqrt{22}}{18}$ $x =\dfrac{5 \pm 2\sqrt{22}}{9}$ |
185 | Let $f(x) = -2x^{2}+x+9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}+x+9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = 1, c = 9$ $ x = \dfrac{-1 \pm \sqrt{1^{2} - 4 \cdot -2 \cdot 9}}{2 \cdot -2}$ $ x = \dfrac{-1 \pm \sqrt{73}}{-4}$ $ x = \dfrac{-1 \pm \sqrt{73}}{-4}$ $x =\dfrac{-1 \pm \sqrt{73}}{-4}$ |
185 | Let $f(x) = -3x^{2}-7x+2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-3x^{2}-7x+2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -3, b = -7, c = 2$ $ x = \dfrac{+ 7 \pm \sqrt{(-7)^{2} - 4 \cdot -3 \cdot 2}}{2 \cdot -3}$ $ x = \dfrac{7 \pm \sqrt{73}}{-6}$ $ x = \dfrac{7 \pm \sqrt{73}}{-6}$ $x =\dfrac{7 \pm \sqrt{73}}{-6}$ |
185 | Let $f(x) = 9x^{2}+7x-4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $9x^{2}+7x-4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 9, b = 7, c = -4$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot 9 \cdot -4}}{2 \cdot 9}$ $ x = \dfrac{-7 \pm \sqrt{193}}{18}$ $ x = \dfrac{-7 \pm \sqrt{193}}{18}$ $x =\dfrac{-7 \pm \sqrt{193}}{18}$ |
185 | Let $f(x) = -x^{2}+5x-1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-x^{2}+5x-1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -1, b = 5, c = -1$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot -1 \cdot -1}}{2 \cdot -1}$ $ x = \dfrac{-5 \pm \sqrt{21}}{-2}$ $ x = \dfrac{-5 \pm \sqrt{21}}{-2}$ $x =\dfrac{-5 \pm \sqrt{21}}{-2}$ |
185 | Let $f(x) = 8x^{2}-2x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $8x^{2}-2x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 8, b = -2, c = -7$ $ x = \dfrac{+ 2 \pm \sqrt{(-2)^{2} - 4 \cdot 8 \cdot -7}}{2 \cdot 8}$ $ x = \dfrac{2 \pm \sqrt{228}}{16}$ $ x = \dfrac{2 \pm 2\sqrt{57}}{16}$ $x =\dfrac{1 \pm \sqrt{57}}{8}$ |
185 | Let $f(x) = -9x^{2}-x+8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}-x+8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = -1, c = 8$ $ x = \dfrac{+ 1 \pm \sqrt{(-1)^{2} - 4 \cdot -9 \cdot 8}}{2 \cdot -9}$ $ x = \dfrac{1 \pm \sqrt{289}}{-18}$ $ x = \dfrac{1 \pm 17}{-18}$ $x =-1,\frac{8}{9}$ |
185 | Let $f(x) = -9x^{2}+7x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}+7x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = 7, c = 6$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot -9 \cdot 6}}{2 \cdot -9}$ $ x = \dfrac{-7 \pm \sqrt{265}}{-18}$ $ x = \dfrac{-7 \pm \sqrt{265}}{-18}$ $x =\dfrac{-7 \pm \sqrt{265}}{-18}$ |
185 | Let $f(x) = 3x^{2}+5x-5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $3x^{2}+5x-5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 3, b = 5, c = -5$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot 3 \cdot -5}}{2 \cdot 3}$ $ x = \dfrac{-5 \pm \sqrt{85}}{6}$ $ x = \dfrac{-5 \pm \sqrt{85}}{6}$ $x =\dfrac{-5 \pm \sqrt{85}}{6}$ |
185 | Let $f(x) = -2x^{2}-7x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}-7x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = -7, c = 1$ $ x = \dfrac{+ 7 \pm \sqrt{(-7)^{2} - 4 \cdot -2 \cdot 1}}{2 \cdot -2}$ $ x = \dfrac{7 \pm \sqrt{57}}{-4}$ $ x = \dfrac{7 \pm \sqrt{57}}{-4}$ $x =\dfrac{7 \pm \sqrt{57}}{-4}$ |
185 | Let $f(x) = -3x^{2}+4x+10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-3x^{2}+4x+10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -3, b = 4, c = 10$ $ x = \dfrac{-4 \pm \sqrt{4^{2} - 4 \cdot -3 \cdot 10}}{2 \cdot -3}$ $ x = \dfrac{-4 \pm \sqrt{136}}{-6}$ $ x = \dfrac{-4 \pm 2\sqrt{34}}{-6}$ $x =\dfrac{-2 \pm \sqrt{34}}{-3}$ |
185 | Let $f(x) = 4x^{2}-x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $4x^{2}-x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 4, b = -1, c = -6$ $ x = \dfrac{+ 1 \pm \sqrt{(-1)^{2} - 4 \cdot 4 \cdot -6}}{2 \cdot 4}$ $ x = \dfrac{1 \pm \sqrt{97}}{8}$ $ x = \dfrac{1 \pm \sqrt{97}}{8}$ $x =\dfrac{1 \pm \sqrt{97}}{8}$ |
185 | Let $f(x) = -8x^{2}-10x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-8x^{2}-10x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -8, b = -10, c = 1$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot -8 \cdot 1}}{2 \cdot -8}$ $ x = \dfrac{10 \pm \sqrt{132}}{-16}$ $ x = \dfrac{10 \pm 2\sqrt{33}}{-16}$ $x =\dfrac{5 \pm \sqrt{33}}{-8}$ |
185 | Let $f(x) = 2x^{2}-10x-8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $2x^{2}-10x-8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 2, b = -10, c = -8$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot 2 \cdot -8}}{2 \cdot 2}$ $ x = \dfrac{10 \pm \sqrt{164}}{4}$ $ x = \dfrac{10 \pm 2\sqrt{41}}{4}$ $x =\dfrac{5 \pm \sqrt{41}}{2}$ |
185 | Let $f(x) = -8x^{2}-5x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-8x^{2}-5x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -8, b = -5, c = 1$ $ x = \dfrac{+ 5 \pm \sqrt{(-5)^{2} - 4 \cdot -8 \cdot 1}}{2 \cdot -8}$ $ x = \dfrac{5 \pm \sqrt{57}}{-16}$ $ x = \dfrac{5 \pm \sqrt{57}}{-16}$ $x =\dfrac{5 \pm \sqrt{57}}{-16}$ |
185 | Let $f(x) = -5x^{2}-10x-3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-5x^{2}-10x-3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -5, b = -10, c = -3$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot -5 \cdot -3}}{2 \cdot -5}$ $ x = \dfrac{10 \pm \sqrt{40}}{-10}$ $ x = \dfrac{10 \pm 2\sqrt{10}}{-10}$ $x =\dfrac{5 \pm \sqrt{10}}{-5}$ |
185 | Let $f(x) = -x^{2}-9x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-x^{2}-9x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -1, b = -9, c = 1$ $ x = \dfrac{+ 9 \pm \sqrt{(-9)^{2} - 4 \cdot -1 \cdot 1}}{2 \cdot -1}$ $ x = \dfrac{9 \pm \sqrt{85}}{-2}$ $ x = \dfrac{9 \pm \sqrt{85}}{-2}$ $x =\dfrac{9 \pm \sqrt{85}}{-2}$ |
185 | Let $f(x) = 3x^{2}+9x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $3x^{2}+9x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 3, b = 9, c = -6$ $ x = \dfrac{-9 \pm \sqrt{9^{2} - 4 \cdot 3 \cdot -6}}{2 \cdot 3}$ $ x = \dfrac{-9 \pm \sqrt{153}}{6}$ $ x = \dfrac{-9 \pm 3\sqrt{17}}{6}$ $x =\dfrac{-3 \pm \sqrt{17}}{2}$ |
185 | Let $f(x) = 7x^{2}+5x-9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}+5x-9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = 5, c = -9$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot 7 \cdot -9}}{2 \cdot 7}$ $ x = \dfrac{-5 \pm \sqrt{277}}{14}$ $ x = \dfrac{-5 \pm \sqrt{277}}{14}$ $x =\dfrac{-5 \pm \sqrt{277}}{14}$ |
185 | Let $f(x) = 6x^{2}-7x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}-7x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = -7, c = -6$ $ x = \dfrac{+ 7 \pm \sqrt{(-7)^{2} - 4 \cdot 6 \cdot -6}}{2 \cdot 6}$ $ x = \dfrac{7 \pm \sqrt{193}}{12}$ $ x = \dfrac{7 \pm \sqrt{193}}{12}$ $x =\dfrac{7 \pm \sqrt{193}}{12}$ |
185 | Let $f(x) = -3x^{2}+3x+3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-3x^{2}+3x+3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -3, b = 3, c = 3$ $ x = \dfrac{-3 \pm \sqrt{3^{2} - 4 \cdot -3 \cdot 3}}{2 \cdot -3}$ $ x = \dfrac{-3 \pm \sqrt{45}}{-6}$ $ x = \dfrac{-3 \pm 3\sqrt{5}}{-6}$ $x =\dfrac{-1 \pm \sqrt{5}}{-2}$ |
185 | Let $f(x) = -6x^{2}-8x+10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-6x^{2}-8x+10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -6, b = -8, c = 10$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot -6 \cdot 10}}{2 \cdot -6}$ $ x = \dfrac{8 \pm \sqrt{304}}{-12}$ $ x = \dfrac{8 \pm 4\sqrt{19}}{-12}$ $x =\dfrac{2 \pm \sqrt{19}}{-3}$ |
185 | Let $f(x) = 7x^{2}+7x-4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}+7x-4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = 7, c = -4$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot 7 \cdot -4}}{2 \cdot 7}$ $ x = \dfrac{-7 \pm \sqrt{161}}{14}$ $ x = \dfrac{-7 \pm \sqrt{161}}{14}$ $x =\dfrac{-7 \pm \sqrt{161}}{14}$ |
185 | Let $f(x) = 8x^{2}-2x-4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $8x^{2}-2x-4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 8, b = -2, c = -4$ $ x = \dfrac{+ 2 \pm \sqrt{(-2)^{2} - 4 \cdot 8 \cdot -4}}{2 \cdot 8}$ $ x = \dfrac{2 \pm \sqrt{132}}{16}$ $ x = \dfrac{2 \pm 2\sqrt{33}}{16}$ $x =\dfrac{1 \pm \sqrt{33}}{8}$ |
185 | Let $f(x) = -7x^{2}-2x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}-2x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = -2, c = 1$ $ x = \dfrac{+ 2 \pm \sqrt{(-2)^{2} - 4 \cdot -7 \cdot 1}}{2 \cdot -7}$ $ x = \dfrac{2 \pm \sqrt{32}}{-14}$ $ x = \dfrac{2 \pm 4\sqrt{2}}{-14}$ $x =\dfrac{1 \pm 2\sqrt{2}}{-7}$ |
185 | Let $f(x) = 10x^{2}-10x-8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $10x^{2}-10x-8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 10, b = -10, c = -8$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot 10 \cdot -8}}{2 \cdot 10}$ $ x = \dfrac{10 \pm \sqrt{420}}{20}$ $ x = \dfrac{10 \pm 2\sqrt{105}}{20}$ $x =\dfrac{5 \pm \sqrt{105}}{10}$ |
185 | Let $f(x) = 7x^{2}+4x-8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}+4x-8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = 4, c = -8$ $ x = \dfrac{-4 \pm \sqrt{4^{2} - 4 \cdot 7 \cdot -8}}{2 \cdot 7}$ $ x = \dfrac{-4 \pm \sqrt{240}}{14}$ $ x = \dfrac{-4 \pm 4\sqrt{15}}{14}$ $x =\dfrac{-2 \pm 2\sqrt{15}}{7}$ |
185 | Let $f(x) = 10x^{2}-4x-10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $10x^{2}-4x-10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 10, b = -4, c = -10$ $ x = \dfrac{+ 4 \pm \sqrt{(-4)^{2} - 4 \cdot 10 \cdot -10}}{2 \cdot 10}$ $ x = \dfrac{4 \pm \sqrt{416}}{20}$ $ x = \dfrac{4 \pm 4\sqrt{26}}{20}$ $x =\dfrac{1 \pm \sqrt{26}}{5}$ |
185 | Let $f(x) = -6x^{2}-9x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-6x^{2}-9x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -6, b = -9, c = 1$ $ x = \dfrac{+ 9 \pm \sqrt{(-9)^{2} - 4 \cdot -6 \cdot 1}}{2 \cdot -6}$ $ x = \dfrac{9 \pm \sqrt{105}}{-12}$ $ x = \dfrac{9 \pm \sqrt{105}}{-12}$ $x =\dfrac{9 \pm \sqrt{105}}{-12}$ |
185 | Let $f(x) = 7x^{2}+7x-3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}+7x-3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = 7, c = -3$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot 7 \cdot -3}}{2 \cdot 7}$ $ x = \dfrac{-7 \pm \sqrt{133}}{14}$ $ x = \dfrac{-7 \pm \sqrt{133}}{14}$ $x =\dfrac{-7 \pm \sqrt{133}}{14}$ |
185 | Let $f(x) = 9x^{2}+10x-10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $9x^{2}+10x-10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 9, b = 10, c = -10$ $ x = \dfrac{-10 \pm \sqrt{10^{2} - 4 \cdot 9 \cdot -10}}{2 \cdot 9}$ $ x = \dfrac{-10 \pm \sqrt{460}}{18}$ $ x = \dfrac{-10 \pm 2\sqrt{115}}{18}$ $x =\dfrac{-5 \pm \sqrt{115}}{9}$ |
185 | Let $f(x) = 9x^{2}-8x-3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $9x^{2}-8x-3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 9, b = -8, c = -3$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot 9 \cdot -3}}{2 \cdot 9}$ $ x = \dfrac{8 \pm \sqrt{172}}{18}$ $ x = \dfrac{8 \pm 2\sqrt{43}}{18}$ $x =\dfrac{4 \pm \sqrt{43}}{9}$ |
185 | Let $f(x) = -7x^{2}-3x+10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}-3x+10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = -3, c = 10$ $ x = \dfrac{+ 3 \pm \sqrt{(-3)^{2} - 4 \cdot -7 \cdot 10}}{2 \cdot -7}$ $ x = \dfrac{3 \pm \sqrt{289}}{-14}$ $ x = \dfrac{3 \pm 17}{-14}$ $x =-\frac{10}{7},1$ |
185 | Let $f(x) = 5x^{2}-8x+3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $5x^{2}-8x+3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 5, b = -8, c = 3$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot 5 \cdot 3}}{2 \cdot 5}$ $ x = \dfrac{8 \pm \sqrt{4}}{10}$ $ x = \dfrac{8 \pm 2}{10}$ $x =1,\frac{3}{5}$ |
185 | Let $f(x) = 2x^{2}+10x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $2x^{2}+10x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 2, b = 10, c = -7$ $ x = \dfrac{-10 \pm \sqrt{10^{2} - 4 \cdot 2 \cdot -7}}{2 \cdot 2}$ $ x = \dfrac{-10 \pm \sqrt{156}}{4}$ $ x = \dfrac{-10 \pm 2\sqrt{39}}{4}$ $x =\dfrac{-5 \pm \sqrt{39}}{2}$ |
185 | Let $f(x) = -4x^{2}-8x-4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}-8x-4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = -8, c = -4$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot -4 \cdot -4}}{2 \cdot -4}$ $ x = \dfrac{8 \pm \sqrt{0}}{-8}$ $ x = \dfrac{8 \pm 0}{-8}$ $x =-1$ |
185 | Let $f(x) = -x^{2}-x+8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-x^{2}-x+8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -1, b = -1, c = 8$ $ x = \dfrac{+ 1 \pm \sqrt{(-1)^{2} - 4 \cdot -1 \cdot 8}}{2 \cdot -1}$ $ x = \dfrac{1 \pm \sqrt{33}}{-2}$ $ x = \dfrac{1 \pm \sqrt{33}}{-2}$ $x =\dfrac{1 \pm \sqrt{33}}{-2}$ |
185 | Let $f(x) = -6x^{2}-5x+7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-6x^{2}-5x+7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -6, b = -5, c = 7$ $ x = \dfrac{+ 5 \pm \sqrt{(-5)^{2} - 4 \cdot -6 \cdot 7}}{2 \cdot -6}$ $ x = \dfrac{5 \pm \sqrt{193}}{-12}$ $ x = \dfrac{5 \pm \sqrt{193}}{-12}$ $x =\dfrac{5 \pm \sqrt{193}}{-12}$ |
185 | Let $f(x) = -10x^{2}+10x+7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-10x^{2}+10x+7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -10, b = 10, c = 7$ $ x = \dfrac{-10 \pm \sqrt{10^{2} - 4 \cdot -10 \cdot 7}}{2 \cdot -10}$ $ x = \dfrac{-10 \pm \sqrt{380}}{-20}$ $ x = \dfrac{-10 \pm 2\sqrt{95}}{-20}$ $x =\dfrac{-5 \pm \sqrt{95}}{-10}$ |
185 | Let $f(x) = -2x^{2}-8x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}-8x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = -8, c = -7$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot -2 \cdot -7}}{2 \cdot -2}$ $ x = \dfrac{8 \pm \sqrt{8}}{-4}$ $ x = \dfrac{8 \pm 2\sqrt{2}}{-4}$ $x =\dfrac{4 \pm \sqrt{2}}{-2}$ |
185 | Let $f(x) = 4x^{2}-4x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $4x^{2}-4x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 4, b = -4, c = 1$ $ x = \dfrac{+ 4 \pm \sqrt{(-4)^{2} - 4 \cdot 4 \cdot 1}}{2 \cdot 4}$ $ x = \dfrac{4 \pm \sqrt{0}}{8}$ $ x = \dfrac{4 \pm 0}{8}$ $x =\frac{1}{2}$ |
185 | Let $f(x) = -5x^{2}+7x+9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-5x^{2}+7x+9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -5, b = 7, c = 9$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot -5 \cdot 9}}{2 \cdot -5}$ $ x = \dfrac{-7 \pm \sqrt{229}}{-10}$ $ x = \dfrac{-7 \pm \sqrt{229}}{-10}$ $x =\dfrac{-7 \pm \sqrt{229}}{-10}$ |
185 | Let $f(x) = 4x^{2}-6x-5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $4x^{2}-6x-5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 4, b = -6, c = -5$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot 4 \cdot -5}}{2 \cdot 4}$ $ x = \dfrac{6 \pm \sqrt{116}}{8}$ $ x = \dfrac{6 \pm 2\sqrt{29}}{8}$ $x =\dfrac{3 \pm \sqrt{29}}{4}$ |
185 | Let $f(x) = 6x^{2}+8x-4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}+8x-4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = 8, c = -4$ $ x = \dfrac{-8 \pm \sqrt{8^{2} - 4 \cdot 6 \cdot -4}}{2 \cdot 6}$ $ x = \dfrac{-8 \pm \sqrt{160}}{12}$ $ x = \dfrac{-8 \pm 4\sqrt{10}}{12}$ $x =\dfrac{-2 \pm \sqrt{10}}{3}$ |
185 | Let $f(x) = 6x^{2}+7x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}+7x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = 7, c = 1$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot 6 \cdot 1}}{2 \cdot 6}$ $ x = \dfrac{-7 \pm \sqrt{25}}{12}$ $ x = \dfrac{-7 \pm 5}{12}$ $x =-\frac{1}{6},-1$ |
185 | Let $f(x) = -7x^{2}+9x+9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}+9x+9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = 9, c = 9$ $ x = \dfrac{-9 \pm \sqrt{9^{2} - 4 \cdot -7 \cdot 9}}{2 \cdot -7}$ $ x = \dfrac{-9 \pm \sqrt{333}}{-14}$ $ x = \dfrac{-9 \pm 3\sqrt{37}}{-14}$ $x =\dfrac{-9 \pm 3\sqrt{37}}{-14}$ |
185 | Let $f(x) = -x^{2}+5x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-x^{2}+5x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -1, b = 5, c = 6$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot -1 \cdot 6}}{2 \cdot -1}$ $ x = \dfrac{-5 \pm \sqrt{49}}{-2}$ $ x = \dfrac{-5 \pm 7}{-2}$ $x =-1,6$ |
185 | Let $f(x) = 6x^{2}-8x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}-8x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = -8, c = -7$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot 6 \cdot -7}}{2 \cdot 6}$ $ x = \dfrac{8 \pm \sqrt{232}}{12}$ $ x = \dfrac{8 \pm 2\sqrt{58}}{12}$ $x =\dfrac{4 \pm \sqrt{58}}{6}$ |
185 | Let $f(x) = 4x^{2}-x-2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $4x^{2}-x-2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 4, b = -1, c = -2$ $ x = \dfrac{+ 1 \pm \sqrt{(-1)^{2} - 4 \cdot 4 \cdot -2}}{2 \cdot 4}$ $ x = \dfrac{1 \pm \sqrt{33}}{8}$ $ x = \dfrac{1 \pm \sqrt{33}}{8}$ $x =\dfrac{1 \pm \sqrt{33}}{8}$ |
185 | Let $f(x) = 10x^{2}+6x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $10x^{2}+6x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 10, b = 6, c = -7$ $ x = \dfrac{-6 \pm \sqrt{6^{2} - 4 \cdot 10 \cdot -7}}{2 \cdot 10}$ $ x = \dfrac{-6 \pm \sqrt{316}}{20}$ $ x = \dfrac{-6 \pm 2\sqrt{79}}{20}$ $x =\dfrac{-3 \pm \sqrt{79}}{10}$ |
185 | Let $f(x) = -3x^{2}-3x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-3x^{2}-3x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -3, b = -3, c = 1$ $ x = \dfrac{+ 3 \pm \sqrt{(-3)^{2} - 4 \cdot -3 \cdot 1}}{2 \cdot -3}$ $ x = \dfrac{3 \pm \sqrt{21}}{-6}$ $ x = \dfrac{3 \pm \sqrt{21}}{-6}$ $x =\dfrac{3 \pm \sqrt{21}}{-6}$ |
185 | Let $f(x) = 7x^{2}-6x-1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $7x^{2}-6x-1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 7, b = -6, c = -1$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot 7 \cdot -1}}{2 \cdot 7}$ $ x = \dfrac{6 \pm \sqrt{64}}{14}$ $ x = \dfrac{6 \pm 8}{14}$ $x =1,-\frac{1}{7}$ |
185 | Let $f(x) = -7x^{2}+2x+10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}+2x+10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = 2, c = 10$ $ x = \dfrac{-2 \pm \sqrt{2^{2} - 4 \cdot -7 \cdot 10}}{2 \cdot -7}$ $ x = \dfrac{-2 \pm \sqrt{284}}{-14}$ $ x = \dfrac{-2 \pm 2\sqrt{71}}{-14}$ $x =\dfrac{-1 \pm \sqrt{71}}{-7}$ |
185 | Let $f(x) = -4x^{2}+4x+7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}+4x+7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = 4, c = 7$ $ x = \dfrac{-4 \pm \sqrt{4^{2} - 4 \cdot -4 \cdot 7}}{2 \cdot -4}$ $ x = \dfrac{-4 \pm \sqrt{128}}{-8}$ $ x = \dfrac{-4 \pm 8\sqrt{2}}{-8}$ $x =\dfrac{-1 \pm 2\sqrt{2}}{-2}$ |
185 | Let $f(x) = 6x^{2}-3x-4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}-3x-4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = -3, c = -4$ $ x = \dfrac{+ 3 \pm \sqrt{(-3)^{2} - 4 \cdot 6 \cdot -4}}{2 \cdot 6}$ $ x = \dfrac{3 \pm \sqrt{105}}{12}$ $ x = \dfrac{3 \pm \sqrt{105}}{12}$ $x =\dfrac{3 \pm \sqrt{105}}{12}$ |
185 | Let $f(x) = -6x^{2}+9x+4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-6x^{2}+9x+4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -6, b = 9, c = 4$ $ x = \dfrac{-9 \pm \sqrt{9^{2} - 4 \cdot -6 \cdot 4}}{2 \cdot -6}$ $ x = \dfrac{-9 \pm \sqrt{177}}{-12}$ $ x = \dfrac{-9 \pm \sqrt{177}}{-12}$ $x =\dfrac{-9 \pm \sqrt{177}}{-12}$ |
185 | Let $f(x) = -4x^{2}+9x+7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}+9x+7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = 9, c = 7$ $ x = \dfrac{-9 \pm \sqrt{9^{2} - 4 \cdot -4 \cdot 7}}{2 \cdot -4}$ $ x = \dfrac{-9 \pm \sqrt{193}}{-8}$ $ x = \dfrac{-9 \pm \sqrt{193}}{-8}$ $x =\dfrac{-9 \pm \sqrt{193}}{-8}$ |
185 | Let $f(x) = -9x^{2}+2x+5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}+2x+5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = 2, c = 5$ $ x = \dfrac{-2 \pm \sqrt{2^{2} - 4 \cdot -9 \cdot 5}}{2 \cdot -9}$ $ x = \dfrac{-2 \pm \sqrt{184}}{-18}$ $ x = \dfrac{-2 \pm 2\sqrt{46}}{-18}$ $x =\dfrac{-1 \pm \sqrt{46}}{-9}$ |
185 | Let $f(x) = -2x^{2}-6x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}-6x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = -6, c = 1$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot -2 \cdot 1}}{2 \cdot -2}$ $ x = \dfrac{6 \pm \sqrt{44}}{-4}$ $ x = \dfrac{6 \pm 2\sqrt{11}}{-4}$ $x =\dfrac{3 \pm \sqrt{11}}{-2}$ |
185 | Let $f(x) = -2x^{2}-4x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-2x^{2}-4x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -2, b = -4, c = 6$ $ x = \dfrac{+ 4 \pm \sqrt{(-4)^{2} - 4 \cdot -2 \cdot 6}}{2 \cdot -2}$ $ x = \dfrac{4 \pm \sqrt{64}}{-4}$ $ x = \dfrac{4 \pm 8}{-4}$ $x =-3,1$ |
185 | Let $f(x) = 10x^{2}+5x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $10x^{2}+5x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 10, b = 5, c = -7$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot 10 \cdot -7}}{2 \cdot 10}$ $ x = \dfrac{-5 \pm \sqrt{305}}{20}$ $ x = \dfrac{-5 \pm \sqrt{305}}{20}$ $x =\dfrac{-5 \pm \sqrt{305}}{20}$ |
185 | Let $f(x) = -4x^{2}-10x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}-10x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = -10, c = -6$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot -4 \cdot -6}}{2 \cdot -4}$ $ x = \dfrac{10 \pm \sqrt{4}}{-8}$ $ x = \dfrac{10 \pm 2}{-8}$ $x =-\frac{3}{2},-1$ |
185 | Let $f(x) = -4x^{2}+10x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}+10x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = 10, c = 6$ $ x = \dfrac{-10 \pm \sqrt{10^{2} - 4 \cdot -4 \cdot 6}}{2 \cdot -4}$ $ x = \dfrac{-10 \pm \sqrt{196}}{-8}$ $ x = \dfrac{-10 \pm 14}{-8}$ $x =-\frac{1}{2},3$ |
185 | Let $f(x) = x^{2}-6x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $x^{2}-6x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 1, b = -6, c = 6$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$ $ x = \dfrac{6 \pm \sqrt{12}}{2}$ $ x = \dfrac{6 \pm 2\sqrt{3}}{2}$ $x =3 \pm \sqrt{3}$ |
185 | Let $f(x) = -3x^{2}-2x+9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-3x^{2}-2x+9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -3, b = -2, c = 9$ $ x = \dfrac{+ 2 \pm \sqrt{(-2)^{2} - 4 \cdot -3 \cdot 9}}{2 \cdot -3}$ $ x = \dfrac{2 \pm \sqrt{112}}{-6}$ $ x = \dfrac{2 \pm 4\sqrt{7}}{-6}$ $x =\dfrac{1 \pm 2\sqrt{7}}{-3}$ |
185 | Let $f(x) = -8x^{2}+6x+8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-8x^{2}+6x+8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -8, b = 6, c = 8$ $ x = \dfrac{-6 \pm \sqrt{6^{2} - 4 \cdot -8 \cdot 8}}{2 \cdot -8}$ $ x = \dfrac{-6 \pm \sqrt{292}}{-16}$ $ x = \dfrac{-6 \pm 2\sqrt{73}}{-16}$ $x =\dfrac{-3 \pm \sqrt{73}}{-8}$ |
185 | Let $f(x) = -3x^{2}-x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-3x^{2}-x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -3, b = -1, c = 6$ $ x = \dfrac{+ 1 \pm \sqrt{(-1)^{2} - 4 \cdot -3 \cdot 6}}{2 \cdot -3}$ $ x = \dfrac{1 \pm \sqrt{73}}{-6}$ $ x = \dfrac{1 \pm \sqrt{73}}{-6}$ $x =\dfrac{1 \pm \sqrt{73}}{-6}$ |
185 | Let $f(x) = x^{2}-3x-1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $x^{2}-3x-1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 1, b = -3, c = -1$ $ x = \dfrac{+ 3 \pm \sqrt{(-3)^{2} - 4 \cdot 1 \cdot -1}}{2 \cdot 1}$ $ x = \dfrac{3 \pm \sqrt{13}}{2}$ $ x = \dfrac{3 \pm \sqrt{13}}{2}$ $x =\dfrac{3 \pm \sqrt{13}}{2}$ |
185 | Let $f(x) = 8x^{2}+7x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $8x^{2}+7x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 8, b = 7, c = -6$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot 8 \cdot -6}}{2 \cdot 8}$ $ x = \dfrac{-7 \pm \sqrt{241}}{16}$ $ x = \dfrac{-7 \pm \sqrt{241}}{16}$ $x =\dfrac{-7 \pm \sqrt{241}}{16}$ |
185 | Let $f(x) = -10x^{2}+3x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-10x^{2}+3x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -10, b = 3, c = 6$ $ x = \dfrac{-3 \pm \sqrt{3^{2} - 4 \cdot -10 \cdot 6}}{2 \cdot -10}$ $ x = \dfrac{-3 \pm \sqrt{249}}{-20}$ $ x = \dfrac{-3 \pm \sqrt{249}}{-20}$ $x =\dfrac{-3 \pm \sqrt{249}}{-20}$ |
185 | Let $f(x) = 4x^{2}+6x-9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $4x^{2}+6x-9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 4, b = 6, c = -9$ $ x = \dfrac{-6 \pm \sqrt{6^{2} - 4 \cdot 4 \cdot -9}}{2 \cdot 4}$ $ x = \dfrac{-6 \pm \sqrt{180}}{8}$ $ x = \dfrac{-6 \pm 6\sqrt{5}}{8}$ $x =\dfrac{-3 \pm 3\sqrt{5}}{4}$ |
185 | Let $f(x) = -7x^{2}+2x+3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}+2x+3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = 2, c = 3$ $ x = \dfrac{-2 \pm \sqrt{2^{2} - 4 \cdot -7 \cdot 3}}{2 \cdot -7}$ $ x = \dfrac{-2 \pm \sqrt{88}}{-14}$ $ x = \dfrac{-2 \pm 2\sqrt{22}}{-14}$ $x =\dfrac{-1 \pm \sqrt{22}}{-7}$ |
185 | Let $f(x) = 9x^{2}+9x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $9x^{2}+9x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 9, b = 9, c = 1$ $ x = \dfrac{-9 \pm \sqrt{9^{2} - 4 \cdot 9 \cdot 1}}{2 \cdot 9}$ $ x = \dfrac{-9 \pm \sqrt{45}}{18}$ $ x = \dfrac{-9 \pm 3\sqrt{5}}{18}$ $x =\dfrac{-3 \pm \sqrt{5}}{6}$ |
185 | Let $f(x) = -7x^{2}+7x+9$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}+7x+9 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = 7, c = 9$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot -7 \cdot 9}}{2 \cdot -7}$ $ x = \dfrac{-7 \pm \sqrt{301}}{-14}$ $ x = \dfrac{-7 \pm \sqrt{301}}{-14}$ $x =\dfrac{-7 \pm \sqrt{301}}{-14}$ |
185 | Let $f(x) = -9x^{2}-5x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}-5x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = -5, c = 1$ $ x = \dfrac{+ 5 \pm \sqrt{(-5)^{2} - 4 \cdot -9 \cdot 1}}{2 \cdot -9}$ $ x = \dfrac{5 \pm \sqrt{61}}{-18}$ $ x = \dfrac{5 \pm \sqrt{61}}{-18}$ $x =\dfrac{5 \pm \sqrt{61}}{-18}$ |
185 | Let $f(x) = x^{2}-8x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $x^{2}-8x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 1, b = -8, c = -6$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot 1 \cdot -6}}{2 \cdot 1}$ $ x = \dfrac{8 \pm \sqrt{88}}{2}$ $ x = \dfrac{8 \pm 2\sqrt{22}}{2}$ $x =4 \pm \sqrt{22}$ |
185 | Let $f(x) = -7x^{2}-10x+4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}-10x+4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = -10, c = 4$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot -7 \cdot 4}}{2 \cdot -7}$ $ x = \dfrac{10 \pm \sqrt{212}}{-14}$ $ x = \dfrac{10 \pm 2\sqrt{53}}{-14}$ $x =\dfrac{5 \pm \sqrt{53}}{-7}$ |
185 | Let $f(x) = 10x^{2}-6x-5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $10x^{2}-6x-5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 10, b = -6, c = -5$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot 10 \cdot -5}}{2 \cdot 10}$ $ x = \dfrac{6 \pm \sqrt{236}}{20}$ $ x = \dfrac{6 \pm 2\sqrt{59}}{20}$ $x =\dfrac{3 \pm \sqrt{59}}{10}$ |
185 | Let $f(x) = 6x^{2}+4x-3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $6x^{2}+4x-3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 6, b = 4, c = -3$ $ x = \dfrac{-4 \pm \sqrt{4^{2} - 4 \cdot 6 \cdot -3}}{2 \cdot 6}$ $ x = \dfrac{-4 \pm \sqrt{88}}{12}$ $ x = \dfrac{-4 \pm 2\sqrt{22}}{12}$ $x =\dfrac{-2 \pm \sqrt{22}}{6}$ |
185 | Let $f(x) = 3x^{2}+6x-2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $3x^{2}+6x-2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 3, b = 6, c = -2$ $ x = \dfrac{-6 \pm \sqrt{6^{2} - 4 \cdot 3 \cdot -2}}{2 \cdot 3}$ $ x = \dfrac{-6 \pm \sqrt{60}}{6}$ $ x = \dfrac{-6 \pm 2\sqrt{15}}{6}$ $x =\dfrac{-3 \pm \sqrt{15}}{3}$ |
185 | Let $f(x) = x^{2}+8x+3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $x^{2}+8x+3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 1, b = 8, c = 3$ $ x = \dfrac{-8 \pm \sqrt{8^{2} - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$ $ x = \dfrac{-8 \pm \sqrt{52}}{2}$ $ x = \dfrac{-8 \pm 2\sqrt{13}}{2}$ $x =-4 \pm \sqrt{13}$ |
185 | Let $f(x) = -4x^{2}+5x+4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}+5x+4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = 5, c = 4$ $ x = \dfrac{-5 \pm \sqrt{5^{2} - 4 \cdot -4 \cdot 4}}{2 \cdot -4}$ $ x = \dfrac{-5 \pm \sqrt{89}}{-8}$ $ x = \dfrac{-5 \pm \sqrt{89}}{-8}$ $x =\dfrac{-5 \pm \sqrt{89}}{-8}$ |
185 | Let $f(x) = 8x^{2}-x-7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $8x^{2}-x-7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 8, b = -1, c = -7$ $ x = \dfrac{+ 1 \pm \sqrt{(-1)^{2} - 4 \cdot 8 \cdot -7}}{2 \cdot 8}$ $ x = \dfrac{1 \pm \sqrt{225}}{16}$ $ x = \dfrac{1 \pm 15}{16}$ $x =1,-\frac{7}{8}$ |
185 | Let $f(x) = 5x^{2}-10x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $5x^{2}-10x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 5, b = -10, c = -6$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot 5 \cdot -6}}{2 \cdot 5}$ $ x = \dfrac{10 \pm \sqrt{220}}{10}$ $ x = \dfrac{10 \pm 2\sqrt{55}}{10}$ $x =\dfrac{5 \pm \sqrt{55}}{5}$ |
185 | Let $f(x) = -5x^{2}-6x+6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-5x^{2}-6x+6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -5, b = -6, c = 6$ $ x = \dfrac{+ 6 \pm \sqrt{(-6)^{2} - 4 \cdot -5 \cdot 6}}{2 \cdot -5}$ $ x = \dfrac{6 \pm \sqrt{156}}{-10}$ $ x = \dfrac{6 \pm 2\sqrt{39}}{-10}$ $x =\dfrac{3 \pm \sqrt{39}}{-5}$ |
185 | Let $f(x) = 4x^{2}+8x-6$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )? | The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $4x^{2}+8x-6 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 4, b = 8, c = -6$ $ x = \dfrac{-8 \pm \sqrt{8^{2} - 4 \cdot 4 \cdot -6}}{2 \cdot 4}$ $ x = \dfrac{-8 \pm \sqrt{160}}{8}$ $ x = \dfrac{-8 \pm 4\sqrt{10}}{8}$ $x =\dfrac{-2 \pm \sqrt{10}}{2}$ |
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