Question

# Out of the two roots of x2+(1−2λ)x+(λ2−λ−2)=0 one root is greater than 3 and the other root is less then 3, then the limits of λ are λ<2 2<λ<5 λ>5 λ=5/2

Solution

## The correct option is B 2<λ<5 x2+(1−2λ)x+(λ2−λ−2)=0              -----------------(1) a = 1 of α,β are roots of (1),  if α<3<β⇒a.f(3)<0 ⇒f(3)<0 ⇒9+(1−2λ)3+λ2−λ−2<0 ⇒λ∈(2,5)

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