Question 23
Consider all polynomials of a complex variable, $P(z) = 4z^4 + az^3$ $+ bz^2 + cz + d,$ where $a,$ $b,$ $c,$ and $d$ are integers, $0 \le d \le c \le b \le a \le 4,$ and the polynomial has a zero $z_0$ with $|z_0| = 1.$ What is the sum of all values $P(1)$ over all the polynomials with these properties?