Question 10
There are nonzero integers $a,$ $b,$ $r,$ and $s$ such that the complex number $r + si$ is a zero of the polynomial $P(x) = x^3 - ax^2 + bx - 65.$ For each possible combination of $a$ and $b,$ let $p_{a,b}$ be the sum of the zeros of $P(x).$ Find the sum of the $p_{a,b}$’s for all possible combinations of $a$ and $b.$