AMC 12 2005b Problem 12

The quadratic equation $x^2+mx+n$ has roots twice those of $x^2+px+m$, and none of $m,n,$ and $p$ is zero. What is the value of $n/p$?

\textbf{(A)}\ 1 \textbf{(B)}\ 2 \textbf{(C)}\ 4 \textbf{(D)}\ 8 \textbf{(E)}\ 16