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2015 AMC 12A Problems/Problem 24

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Problem

The zeroes of the function $f(x)=x^2-ax+2a$ are integers. What is the sum of all possible values of $a$?

$\textbf{(A) }7\qquad\textbf{(B) }8\qquad\textbf{(C) }16\qquad\textbf{(D) }17\qquad\textbf{(E) }18$

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