Question 21
Let $p(x) = x^3 + ax^2 + bx + c,$ where $a,$ $b,$ and $c$ are complex numbers. Suppose that $$
\begin{gathered} p(2009 + 9002\pi i) \\ = p(2009) \\ = p(9002) = 0. \end{gathered}
$$ What is the number of nonreal zeros of $x^{12} + ax^8 + bx^4 + c?$
\begin{gathered} p(2009 + 9002\pi i) \\ = p(2009) \\ = p(9002) = 0. \end{gathered}
$$ What is the number of nonreal zeros of $x^{12} + ax^8 + bx^4 + c?$