Question

If the equation $\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ has roots equal in magnitude but opposite in sign, then m =

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ $\Rightarrow$ $x^2-bx=\frac{m-1}{m+1}(ax-c)$

$\Rightarrow$ $x^2-(b+\frac{m-1}{m+1}a)x+c\left(\frac{m-1}{m+1}\right)=0$

If roots are equal in magnitude but opposite in sign then sum of roots is zero

$\Rightarrow$ $(b+\frac{m-1}{m+1}a)$ = 0 $\Rightarrow$ m = $\frac{a-b}{a+b}$