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1972 AMC 12 Question 22

AMC12 · 1972 AMC 12

Question 22

If $a\pm bi$ $(b\ne0)$ are imaginary roots of the equation $x^3+qx+r=0,$ where $a,$ $b,$ $q,$ and $r$ are real numbers, then $q$ in terms of $a$ and $b$ is:
  1. $a^2+b^2$
  2. $2a^2-b^2$
  3. $b^2-a^2$
  4. $b^2-2a^2$
  5. $b^2-3a^2$