1963 AHSME Problem 14

Given the equations x^2+kx+6=0 and x^2-kx+6=0. If, when the roots of the equation are suitably listed, each root of the second equation is 5 more than the corresponding root of the first equation, then k equals:

\textbf{(A)}\ 5 \qquad \textbf{(B)}\ -5 \qquad \textbf{(C)}\ 7 \qquad \textbf{(D)}\ -7 \qquad \textbf{(E)}\ \text{none of these}

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