1952 AHSME Problem 23

If \frac{x^2-bx}{ax-c}=\frac{m-1}{m+1} has roots which are numerically equal but of opposite signs, the value of m must be:

\textbf{(A) \ }\frac{a-b}{a+b} \qquad \textbf{(B) \ }\frac{a+b}{a-b} \qquad \textbf{(C) \ }c \qquad \textbf{(D) \ }\frac{1}{c} \qquad \textbf{(E) \ }1

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