AHSME 1951 Problem 47

If $r$ and $s$ are the roots of the equation $ax^2+bx+c=0$, the value of $\frac{1}{r^{2}}+\frac{1}{s^{2}}$ is: $\textbf{(A)}\ b^{2}-4ac \textbf{(B)}\ \frac{b^{2}-4ac}{2a} \textbf{(C)}\ \frac{b^{2}-4ac}{c^{2}} \textbf{(D)}\ \frac{b^{2}-2ac}{c^{2}}$ $\textbf{(E)}\ \text{none of these}$