Problem

4. $f(z) = 2z^4 - 19z^3 + Az^2 + Bz - 156$

where $A$ and $B$ are constants.

The complex number $5 - i$ is a root of the equation $f(z) = 0$

(a) Write down another complex root of this equation.

(b) Solve the equation $f(z) = 0$ completely.

(c) Determine the value of $A$ and the value of $B$.