Q.

α,β,γ are the roots of the equation x3-10x2+7x+8=0.
Match the following.
List - I                                                 List - II

 I)  α+β+γ                                      a)  -434

II)  α2+β2+γ2                                b)  -78

III)  1α+1β+1γ                             c)  86

IV)  αβγ+βγα+γαβ                     d)  0 


                                                           e)  10

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a

e, c, b, a

b

d, c, a, b

c

e, c, a, b

d

e, b, c, a

answer is C.

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Detailed Solution

Ifα,β,γarerootsofx310x2+7x+8=0α+β+γ=10(α+β+γ)2=100α2+β2+γ2+2(αβ+βγ+γα)=100α2+β2+γ2=1002(7)10014=861α+1β+1γ=αβ+βγ+γααβγ78αβγ+βγα+γαβ=α2+β2+γ2αβγ868434

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α,β,γ are the roots of the equation x3-10x2+7x+8=0.Match the following.List - I                                                 List - II I)  α+β+γ                                      a)  -434II)  α2+β2+γ2                                b)  -78III)  1α+1β+1γ                             c)  86IV)  αβγ+βγα+γαβ                     d)  0                                                            e)  10