Question

If one root of the equation 4x² − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
(a)8
(b)−8
(c)4
(d)−4

Answer 1

SOLUTION :  

Option (a) is correct : 8  

Given : 4x² - 2x + (λ - 4) = 0

Let α be the one root and other root be 1/α

On comparing the given equation with ax² + bx + c = 0  

Here, a = 4 , b = - 2 , c = (λ - 4)

Product of zeroes = c/a  

α × 1/α = (λ - 4)/4

1 =  (λ - 4)/4

4 =  (λ - 4)

λ = 4 + 4  

λ = 8  

Hence, the value of  λ is 8 .

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Answer 2

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

(a)8

(b)−8If one root of the equation 4x² − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =

(a)8√√√√√

(b)−8

(c)4

(d)−4