Multiple choice

Find an equation whose roots are negative of the roots of $x^2 + 5x + 6 = 0$

  1. $x^2 - 3x + 2 = 0$
  2. $x^2 + 6x - 5 = 0$
  3. $x^2 - 5x + 6 = 0$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If roots of x^2 + 5x + 6 = 0 are r1, r2, then r1+r2 = -5 and r1*r2 = 6. The new roots are -r1 and -r2. The new sum is -(r1+r2) = 5. The new product is (-r1)*(-r2) = 6. The equation is x^2 - 5x + 6 = 0.

AI explanation

To find an equation whose roots are the negative of the original roots, substitute -x for x in the given equation. Applying this to x^2 + 5x + 6 = 0 yields (-x)^2 + 5(-x) + 6 = 0. Simplifying this results in x^2 - 5x + 6 = 0.

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