AHSME 1961 Problem 29

Let the roots of $ax^2+bx+c=0$ be $r$ and $s$. The equation with roots $ar+b$ and $as+b$ is: $\textbf{(A)}\ x^2-bx-ac=0 \textbf{(B)}\ x^2-bx+ac=0 \\ \textbf{(C)}\ x^2+3bx+ca+2b^2=0 \textbf{(D)}\ x^2+3bx-ca+2b^2=0 \\ \textbf{(E)}\ x^2+bx(2-a)+a^2c+b^2(a+1)=0$