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If One Root of the Equation 4x2 − 2x + (λ − 4) = 0 Be the Reciprocal of the Other, Then λ = - CBSE Class 10 - Mathematics

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Question

If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =

  • 8

  • -8

  • 4

  • -4

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`.

  Is there an error in this question or solution?

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Solution If One Root of the Equation 4x2 − 2x + (λ − 4) = 0 Be the Reciprocal of the Other, Then λ = Concept: Solutions of Quadratic Equations by Factorization.
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