Multiple choice

Two candidates attempt to solve a quadratic equation $\displaystyle x^{2} + px + q = 0$. One starts with a wrong value of $\displaystyle p$ and gets $2$, $6$ as its roots and other starts with wrong value of $\displaystyle q$ and obtains roots $2$, $-9$. The correct roots are

  1. $-3, \: -4$
  2. $3, \: 4$
  3. $-3, \: 4$
  4. $-4, \: 3$
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A Correct answer
Explanation

First candidate gets roots 2, 6, so x^2 - 8x + 12 = 0. q is correct, so q = 12. Second candidate gets roots 2, -9, so x^2 + 7x - 18 = 0. p is correct, so p = 7. Correct equation is x^2 + 7x + 12 = 0. Roots are (x+3)(x+4) = 0, so -3, -4.

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