Question

If the roots of equation $\frac{x^2-bx}{ax-c}$ = $\frac{m-1}{m+1}$ are equal but opposite in sign, then the value of m will be

• A. $\frac{b-a}{a+b}$
• B. $\frac{a+b}{a-b}$
• C. $\frac{b+a}{b-a}$
• D. $\frac{a-b}{a+b}$

Answer 1

The correct option is D

$\frac{a-b}{a+b}$

Given equation can be written as

(m+1)$x^2$ - {m(a + b) - (a - b)}$x$ + c(m - 1) = 0

Roots are equal and of opposite sign. so sum of roots is equal to zero.

⇒ $0=m(a+b)-(a-b)\Rightarrow m=\frac{a-b}{a+b}$