Form the quadratic equation if its roots are: $5$ and $-7$
- $x^2\,+\,2x\,-\,35\,=\,0$
- $x^2\,+\,x\,-\,35\,=\,0$
- $x^2\,+\,3x\,-\,35\,=\,0$
- $x^2\,+\,4x\,-\,35\,=\,0$
Reveal answer
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A
Correct answer
Explanation
A quadratic equation with roots r1 and r2 is given by x^2 - (r1 + r2)x + (r1 * r2) = 0. Here, roots are 5 and -7, so the sum is -2 and the product is -35. The equation is x^2 - (-2)x + (-35) = 0, which is x^2 + 2x - 35 = 0.
AI explanation
For the roots 5 and -7, the sum is 5 + -7 = -2 and the product is 5 times -7 = -35. Substituting these into the quadratic equation formula x^2 - (sum)x + (product) = 0 gives x^2 - (-2)x + -35 = 0. This simplifies to x^2 + 2x - 35 = 0.