Multiple choice

If ${8,2}$ are the roots of $x^2+ax+\beta =0$ and ${3, 3}$ are the roots of $x^2+\alpha x +b=0$, then the roots of the equation $x^2+ax+b=0$ are:

  1. $1, -1$
  2. $-9, 2$
  3. $-8, -2$
  4. $9, 1$
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D Correct answer
Explanation

From roots {8, 2}, x^2 - 10x + 16 = 0, so a = -10. From roots {3, 3}, x^2 - 6x + 9 = 0, so b = 9. The equation x^2 + ax + b = 0 becomes x^2 - 10x + 9 = 0. Factoring gives (x-9)(x-1) = 0, so roots are 9 and 1.

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