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


If one root of the equation $4 x^{2}-2 x+(\lambda-4)=0$ be the reciprocal of the other, then $\lambda=$

(a) 8
(b) −8
(c) 4
(d) −4


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




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

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

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

And the product of the roots

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





Therefore, value of $\lambda=8$

Thus, the correct answer is


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