2013 AIME I Problem 10

There are nonzero integers a, b, r, and s such that the complex number r+s i is a zero of the polynomial P(x)=x^{3}-a x^{2}+b x-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.