1958 AHSME Problem 11

The number of roots satisfying the equation \sqrt{5 - x} = x\sqrt{5 - x} is:

\textbf{(A)}\ \text{unlimited}\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ 1\qquad \textbf{(E)}\ 0

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