Multiple choice

The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of $13$ and the roots thus found was $-2$ and $-15$. Then the roots of the correct equation are

  1. $-3,10$
  2. $-3,-10$
  3. $3,-10$

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

Roots -2 and -15 imply (x+2)(x+15) = x^2 + 17x + 30 = 0. The wrong coefficient was 17, so the correct equation is x^2 + 13x + 30 = 0. Factoring gives (x+3)(x+10) = 0, so roots are -3 and -10.

AI explanation

Use the sum of roots to find the correct coefficient by solving -2 + (-15) = 17, which gives the constant term q as 30. The correct coefficient of x is p = 13. The correct quadratic equation is x^2 + 13x + 30 = 0, which factors into (x + 3)(x + 10) = 0. The roots of the correct equation are -3 and -10.

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