f(0)⋅f(1)≤0
⇒2(λ2+1−4λ+2)≤0⇒2(λ2−4λ+3)≤0
⇒(λ−1)(λ−3)≤0
⇒λ∈[1,3]
But at λ=1, both roots are 1.
So, λ=1
The set of all real values of λ for which the quadratic equation (λ2+1)x2−4λx+2=0 always have exactly one root in the interval (0,1) is :
Held on 3 Sept 2020 · Verified 6 Jul 2026.
(−3,−1)
(0,2)
(1,3]
(2,4]
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