1964 AHSME Problem 7

Let n be the number of real values of p for which the roots of x^2-px+p=0 are equal. Then n equals:

\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ \text{a finite number greater than 2}\qquad \textbf{(E)}\ \infty

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