Multiple choice

Find a quadratic equation whose roots $x_1$ and $x_2$ satisfy the condition $x_1^2 + x_2^2 = 5, 3 (x_1^5+x_2^5) = 11 (x_1^3 + x_2^3)$. (Assume that $x_1, x_2$ are real)

  1. $x^2 \pm 3x + 2 = 0$
  2. $x^2 \pm 6x + 12 = 0$
  3. $x^2 \pm 9x + 12 = 0$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given x1^2 + x2^2 = 5. Let s = x1+x2, p = x1*x2. s^2 - 2p = 5. Using the second condition 3(x1^5+x2^5) = 11(x1^3+x2^3), we can solve for s and p. The resulting quadratic is x^2 - sx + p = 0. Testing option A: x^2 - 3x + 2 = 0, roots 1, 2. 1^2+2^2 = 5. 3(1+32) = 99, 11(1+8) = 99. Matches.

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