Multiple choice

Find the complete quadratic equation in $x$, whose solutions are $-7$ and $5$.

  1. $x^{2}+ 2x - 35$
  2. $x^{2}+ 2x + 35$
  3. $x^{2}+ 2x $
  4. $x^{2}- 35$
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A Correct answer
Explanation

If roots are -7 and 5, the equation is (x - (-7))(x - 5) = (x + 7)(x - 5) = x^2 - 5x + 7x - 35 = x^2 + 2x - 35 = 0.

AI explanation

A quadratic equation with roots r1 and r2 can be formed using the identity (x - r1)(x - r2) = 0. Substituting the given roots -7 and 5 gives (x + 7)(x - 5). Expanding this product yields x^2 - 5x + 7x - 35, which simplifies to x^2 + 2x - 35. The complete quadratic equation is x^2 + 2x - 35 = 0.

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