1965 AHSME Problem 22

If a_2 \neq 0 and r and s are the roots of a_0 + a_1x + a_2x^2 = 0, then the equality a_0 + a_1x + a_2x^2 = a_0\left (1 - \frac {x}{r} \right ) \left (1 - \frac {x}{s} \right ) holds:

\begin{array}{l} \textbf{(A)}\ \text{for all values of }x, a_0\neq 0 \qquad \textbf{(B) }\ \text{for all values of }x \\ \textbf{(C) }\ \text{only when }x = 0 \qquad \textbf{(D) }\ \text{only when }x = r \text{ or }x = s \\ \textbf{(E) }\ \text{only when }x = r \text{ or }x = s, a_0 \neq 0 \end{array}

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