Let $a$ and $b$ be real numbers. Among the four roots of \[z^4 + 4iz^3 - 24z^2 + aiz + b = 0,\]one has real part 1, and another root has real part $-5.$ Enter all possible values of $b,$ separated by commas.

I know that if I substitute $z=xi.$, I get

\[x^4 + 4x^3 + 24x^2 - ax + b = 0\]

However, I can't figure out how to solve it from there.

Guest Jan 22, 2021

edited by
Guest
Jan 22, 2021