Problem: If ax−cx2−bx=m+1m−1 has roots which are numerically equal but of opposite signs, the value of m must be:
Answer Choices:
A. a+ba−b
B. a−ba+b
C. c
D. c1
E. 1
Solution:
The equation is equivalent to x2−(b+m+1am−1)x+cm+1m−1=0. Since the coefficient of x is equal to the sum of the roots, it must be zero. We have b+m+1m−1a=0.∴bm+b+ma−a=0;
∴m=a+ba−b.