The positive value of λ for which the co-efficient of x 2 in the expansion x 2 x + λ x 2 10 is 720 , is

Step-by-step solution

Coefficient of x 2 in x 2 x + λ x 2 10 = coefficient of x 0 in x + λ x 2 10 A general term in the expansion x + λ x 2 10 is 10 C r x 10 - r λ x 2 r = 10 C r λ r x 5 - 5 r 2 ⇒ coefficient of x 0 =   10 C 2 λ 2 (for r = 2 ) = 45 λ 2 Now 45 λ 2 = 720 ⇒ λ = ± 4