1.

Let t be a real number satifying `2t ^(3) -9t ^(2) + 30 -lamda =0` where `t =x + 1/xand lamda in R.` if the cubic has exactly two real and distinct solutions for x then exhaustive set of values 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

Answer» Correct Answer - 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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