1967 AHSME Problem 17

If r_1 and r_2 are the distinct real roots of x^2+px+8=0, then it must follow that:

\begin{array}{l} \textbf{(A)}\ |r_1+r_2|>4\sqrt{2}\qquad \textbf{(B)}\ |r_1|>3 \; \text{or} \; |r_2| >3 \\ \textbf{(C)}\ |r_1|>2 \; \text{and} \; |r_2|>2\qquad \textbf{(D)}\ r_1<0 \; \text{and} \; r_2<0\qquad \textbf{(E)}\ |r_1+r_2|<4\sqrt{2} \end{array}

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