Question

If one root of $4x^2-2x+(\lambda -4)=0$ is reciprocal of the other, then value of $\lambda$ is

• A. 8

Answer 1

The correct option is A 8
It is given that one root of $4x^2-2x+(\lambda -4)=0$ is reciprocal of the other. If $\alpha$ is one root, then $\frac{1}{\alpha }$ will be the another root.

As we know, roots of a quadratic equation $a{x}^2+bx+c=0,a\ne 0$ will be reciprocal to each other if and only if $a=c$.

$\Rightarrow \text{Coefficient of}{x}^2=\text{Constant term}\Rightarrow 4=\lambda -4\Rightarrow \lambda =8$