2015 AMC 12A Problem 18

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

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.