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Q.

Let α,β and γ be the roots of the equation x3−x2+3x+1=0 . Then the value of γ    β    α+2β+2γα    γ    β+2α+2γβ    α    γ+2α+2β is equal to

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a

-10

b

-8

c

7

d

9

answer is B.

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Detailed Solution

Δ=γβα+2β+2γαγβ+2α+2γβαγ+2α+2β Applying C3→C3−2C1−2C2, we get Δ=γβααγββαγ=(α+β+γ)α2+β2+γ2−αβ−βγ−γα=(α+β+γ)(α+β+γ)2−3(αβ+βγ+γα)=1×12−3×(3)=−8
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