Let λ ≠ 0 be in R . If α and β are the roots of the equation, x 2 - x + 2 λ = 0 and α and γ are the roots of the equation, 3 x 2 - 10 x + 27 λ = 0 , then β γ λ is equal to:

Step-by-step solution

Satisfying α we have, 3 α 2 - 10 α + 27 λ = 0     … i and 3 α 2 - 3 α + 6 λ = 0     … ii Subtract - 7 α + 21 λ = 0 3 λ = α by ii , 9 λ 2 - 3 λ + 2 λ = 0 ⇒ λ = 0 , 1 9   but   λ ≠ 0 ∴ Given equation are x 2 - x + 2 9 = 0 and 3 x 2 - 10 x + 3 = 0 ∴ α = 1 3 , β = 2 3 , α = 1 3 , γ = 3 ∴ β γ λ = 2 3 · 3 1 9 = 18