If one root of the equation 4x2 − 2x + (λ − 4) = 0

Solution:

Let $\alpha$ and $\beta$ be the roots of quadratic equation $4 x^{2}-2 x+(\lambda-4)=0$ in such a way that $\alpha=\frac{1}{\beta}$

Here, $a=4, b=-2$ and,$c=(\lambda-4)$

Then, according to question sum of the roots

$\alpha+\beta=\frac{-b}{a}$

$\frac{1}{\beta}+\beta=\frac{-(-2)}{4}$

$\frac{1+\beta^{2}}{\beta}=\frac{1}{2}$

$2+2 \beta^{2}=\beta$

$2+2 \beta^{2}=\beta$

$2 \beta^{2}-\beta+2=0$

And the product of the roots

$\alpha \cdot \beta=\frac{c}{a}$

$1=\frac{\lambda-4}{4}$

$\lambda-4=4$

$\lambda=4+4$

$=8$

Therefore, value of $\lambda=8$

Thus, the correct answer is