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Question
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Options
8
-8
4
-4
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Solution
Let `alpha and beta `be the roots of quadratic equation `4x^2 - 2x + (λ - 4) = 0` in such a way that `alpha = 1/beta`
Here, a = 4,b = -2 and , c= (λ - 4)
Then , according to question sum of the roots
`alpha + beta = (-b)/a`
`1/beta + beta = (-(-2))/4`
`(1+beta^2) = 1/2`
`2 + 2beta^2 = beta`
`2beta^2 - beta + 2 = 0`
And the product of the roots
`alpha . beta = c/a`
`1/beta xx beta = (λ - 4)/4`
`1 = (λ -4)/4`
`λ - 4 = 4`
`λ = 4 + 4`
`= 8`
Therefore, value of `λ = 8`.
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