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Let t be a ral number satifying 2t ^(2) ...

Let t be a ral number satifying `2t ^(2) -9t ^(2) + 30 -lamda =0` where `t =x + 1/xand lamda in R.`
If the above cubic has three real and sisinct solutions foe x then exhaustive set of value of `lamda` be :

A

`lamda epsilon(-oo,3)uu(30,oo)`

B

`lamda epsilon(-oo,-22)uu(10,oo)uu{3}`

C

`lamda epsilon{3,30}`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
b
Since domain of `f(t)=2t^(3)+30,t=x+1//x,|t|ge2f(-2)=-22f(2)=10`, critical points at `t=0` & `3,f(3)=3`
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