# For polynomial lovers!

Algebra Level 5

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 zeros of $$P(x)$$. Find the sum of the $$p_{a,b}$$'s for all the possible combinations of $$a$$ and $$b$$.

Here $$i=\sqrt{-1}$$

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