AHSME 1960 Problem 11

For a given value of $k$ the product of the roots of $x^2-3kx+2k^2-1=0$ is $7$. The roots may be characterized as: $\textbf{(A) }\text{integral and positive} \textbf{(B) }\text{integral and negative} \\ \textbf{(C) }\text{rational, but not integral} \textbf{(D) }\text{irrational} \textbf{(E) } \text{imaginary}$