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

α + β = 1       . . . i α β = 2 λ       . . . ii α + γ = 10 3       . . . iii α γ = 9 λ       . . . iv from iv   &   ii γ β = 9 2       . . . v from iii - i γ - β = 10 3 - 1 = 7 3       . . . vi from v and vi β = 2 3 , γ = 3 from i   α = 1 - β = 1 - 2 3 = 1 3 from ii   λ = α β 2 = 1 3 × 2 3 2 =