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Question

If α,β,γ are the roots of x3+ax2+bx+c=0, then (α+β2γ)=

A
2a39ab+27c
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B
2a3+9ab+27c
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C
2a39ao27c
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D
2a3+9ao27c
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Solution

The correct option is A 2a39ab+27c
As α,β,γ are roots of x3+ax2+bx+c=0
Gives
s1=α+β+γ=aα+β=aγs2=αβ+βγ+γα=bs3=αβγ=c
Therefore,
Π(α+β2γ)=Π(a2γ)=(a+3α)(a+3β)(a+3γ)=(a3+3a2(α+β+γ)+3a(αβ+βγ+γα)+2+αβγ)=(a33a3+9ab27c)=2a39ab+27c

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