The set of all real values of λ for which the quadratic equations. (λ2+1)x2−4λx+2=0always have exactly one root in the interval (0,1) is :

Let f(x)=λ2+1x2-4λx+2If f(x) = 0 has exactly one root in (0,1) then f(0) ⋅f(1) ≤  0  2 ( λ2+1−4λ+2)≤ 0( λ−1) ( λ−3)≤  0 But for λ=1⇒n=1 is a repeat root,  Therefore, λ∈(1,3]