Question

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

Is the answer: 8

Answer 1

Yes

Let f(x) = 4x² - 2x + ($ - 4) = 0 and α and β be its zeroes

Given,

β = 1/α (i)

Product of roots, αβ = c/a

α*1/α = ($ - 4)/4

($ - 4)/4 = 1

$ - 4 = 4

$ = 8

So, value of $ = 8