Let α , β be the roots of the equation x 2 - 4 λ x + 5 = 0 and α , γ be the roots of the equation x 2 - 3 2 + 2 3 x + 7 + 3 λ 3 = 0 . If β + γ = 3 2 , then α + 2 β + γ 2 is equal to

Step-by-step solution

Given α   &   β are roots of x 2 - 4 λ x + 5 = 0 So, α + β = 4 λ and α β = 5 .......(i) And α   &   γ are roots of x 2 - 3 2 + 2 3 x + 7 + 3 λ 3 = 0 So, α + y = 3 2 + 2 3 and α γ = 7 + 3 λ 3 .........(ii) Given, if β + γ = 3 2    So, from equation (i) and (ii) we get, α = 2 λ + 3 and β = 2 λ - 3   , Now by product of roots we get, 4 λ 2 - 3 = 5 ⇒ λ = 2 &