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Question

If α, β, γ are the roots of the equation x3+4x+1=0,then (α+β)1+(β+γ)1+(γ+α)1=


A

2

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B

3

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C

4

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D

5

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Solution

The correct option is C

4


If α,β, γ are the roots of the equation

α+β+γ=0,αβ+βγ+γα=4,αβγ=1

therefore(α+β)1+(β+γ)1+(γ+α)1
=1γ+1α+1β
=(αβ+βγ+γααβγ)
=(41)=4


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