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Question

 If α,β and γ are the roots of the equation x3+3x+2=0 and (αβ)(αγ),(βγ)(βα),(γα)(γβ) are the roots of equation  y39y2216=0 . Express y in terms of α.



Solution

The correct option is B


α,β,γ are the roots of equation x3+3x+2=0  ___________(1)

Sum of the roots α+β+γ=ba=0β+γ=α

Sum of the roots taking two at a time αβ+βγ+γα=ca=3

Product of the roots αβγ=da=2βγ=2α

We can take y = (αβ)(αγ)=α2αβαγ+βγ

=α2α(β+γ)+βγβ+γ=α,βγ=2α

=  α2α(α)+2α

y=2α22α

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