1972 AHSME Problem 22

If a\pm bi~(b\neq 0) 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

\textbf{(A) }a^2+b^2\qquad \textbf{(B) }2a^2-b^2\qquad \textbf{(C) }b^2-a^2\qquad \textbf{(D) }b^2-2a^2\qquad \textbf{(E) }b^2-3a^2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.