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Question

Out of the two roots of x2+(12λ)x+(λ2λ2)=0 one root is greater than 3 and the other root is less then 3, then the limits of λ are


  1. λ<2

  2. 2<λ<5

  3. λ>5

  4. λ=5/2


Solution

The correct option is B

2<λ<5


x2+(12λ)x+(λ2λ2)=0              -----------------(1)

a = 1 of α,β are roots of (1), 

if α<3<βa.f(3)<0

f(3)<0

9+(12λ)3+λ2λ2<0

λ(2,5)

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