Question

If the roots $\alpha$ and $\beta$ of the equation $\frac{x^2-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}$ are such that $\alpha +\beta =0$, then the value of $\lambda$ is

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

Answer 1

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

$\frac{x^2-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}$
$(\lambda +1)x^2-\left[b\right(\lambda +1)+a(\lambda -1\left)\right]x+c(\lambda -1)=0$
Since, $\alpha ,\beta$ are the roots of the given equation
$\alpha +\beta =\frac{b(\lambda +1)+a(\lambda -1)}{\lambda +1}$ ..(i)
Given $\Rightarrow \alpha +\beta =0$ ...(ii)
From (i) and (ii),we get
$\lambda =\frac{a-b}{a+b}$
Hence, option 'D' is correct.