AHSME 1952 Problem 13

The function $x^2+px+q$ with $p$ and $q$ greater than zero has its minimum value when: $\textbf{(A) \ }x=-p \textbf{(B) \ }x=\frac{p}{2} \textbf{(C) \ }x=-2p \textbf{(D) \ }x=\frac{p^2}{4q}$ $\textbf{(E) \ }x=\frac{-p}{2}$