If one root of the equation 4x2-2x+k-4=0 is the reciprocal of the other, then the value of k is

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If one root of the equation $4 x^{2} - 2 x + k - 4 = 0$ is the reciprocal of the other, then the value of k is

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Detailed Solution

$4 x^{2} - 2 x + k - 4 = 0$

One root is $α$ then other root is $\frac{1}{α}$ so,

Product of the roots is $\frac{c}{a}$ then

$\Rightarrow a \times \frac{1}{a} = 1$

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

$k = 8$

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