1958 AHSME Problem 33

For one root of ax^2 + bx + c = 0 to be double the other, the coefficients a,\,b,\,c must be related as follows:

\begin{array}{l} \textbf{(A)}\ 4b^2 = 9c\qquad \textbf{(B)}\ 2b^2 = 9ac\qquad \textbf{(C)}\ 2b^2 = 9a\qquad \\ \textbf{(D)}\ b^2 - 8ac = 0\qquad \textbf{(E)}\ 9b^2 = 2ac \end{array}

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