The number of real values of λ for which the system of linear equations, 2 x + 4 y - λ z = 0 , 4 x + λ y + 2 z = 0 and λ x + 2 y + 2 z = 0 , has infinitely many solutions, is:

Step-by-step solution

For Infinite many solution Δ = 0 i.e , 2 4 - λ 4 λ 2 λ 2 2 = 0   ⇒   2 2 - 2 λ - 4 8 - 2 λ - λ 8 - λ 2 = 0 ⇒ λ 3 + 4 λ - 40 = 0  f ( x ) = x 3 + 4 x - 40 is strictly increasing i.e., equation has only one real root, Also, ∆ 1 = 0 , ∆ 2 = 0 , ∆ 3 = 0 ∴ Only one value of λ is possible