If one root of the equation 4x2 – 2x + (λ – 4) = 0 be the recipro

1.	If one root of the equation 4x2 – 2x + (λ – 4) = 0 be the reciprocal of the other, then k A. 8 B. – 8 C. 4 D. – 4
Answer» Let α and β be the two roots of the given equation 4x² – 2x + (λ – 4) = 0 According to the given condition α = 1/β Here a = 4, b = – 2 and c = (λ – 4) α + β = 2/4 = 1/2 1/β + β = 1/2 α β = \(\frac{k-4}{4}\) \(\frac{1}{\beta}\beta=\frac{k-4}{4}\) K = 8

If one root of the equation 4x2 – 2x + (λ – 4) = 0 be the reciprocal of the other, then k A. 8 B. – 8 C. 4 D. – 4

Answer»

Let α and β be the two roots of the given equation

4x² – 2x + (λ – 4) = 0

According to the given condition

α = 1/β

Here a = 4, b = – 2 and c = (λ – 4)

α + β = 2/4 = 1/2

1/β + β = 1/2

α β = \(\frac{k-4}{4}\)

\(\frac{1}{\beta}\beta=\frac{k-4}{4}\)

K = 8