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Question

If α,β and γ are the roots of the equation x3 + 3x2 + 5x - 6 = 0, find the value of (α1βγ)(β1γα)(γ1αβ)(1α+1β+1γ)1


A

3625

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B

256

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C

12536

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D

36125

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Solution

The correct option is B

256


α,β and γ are the roots of the equation x3 + 3x2 + 5x - 6 = 0

As we know,
α+β+γ=ba=3,
αβ+βγ+γα=5,
αβγ=da=6

Here,
(α1βγ)(β1γα)(γ1αβ)(1α+1β+1γ)1
=(α1βγ)(βγγa)(γ1αβ)(αβγαβ+βγ+γα)=(αβγ1)(αβγ1)(αβγ1)α2β2γ2×αβγ(αβ+βγ+γα)
=(αβγ1)3αβγ(αβ+βγ+γα)=536×5=256


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