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# If One Root of the Equation 4x2 − 2x + (λ − 4) = 0 Be the Reciprocal of the Other, Then λ = - 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.

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