Question

If the roots of the equation $\frac{x^2-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}$ are equal and opposite then the value of $\lambda$ is

• A. $\frac{a-b}{a+b}$
• B. $c$
• C. $\frac{1}{c}$
• D. $\frac{a+b}{a-b}$

Answer 1

The correct option is A $\frac{a-b}{a+b}$

$\frac{x^2-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}$

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

If roots are equal and opposite in sign.

$\therefore$ sum of roots = 0

$\Rightarrow$ $b=a\frac{1-\lambda }{1+\lambda }⟹\lambda =\frac{a-b}{a+b}$