If α,β and γ are roots of 4x3+8x2−x−2=0, then the value of 4(α+1)(β+1)(γ+1)αβγ is

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answer is -6.

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Detailed Solution

4x3+8x2−x−2=4(x−α)(x−β)(x−γ) Putting x=−1, we get 3=4(−1−α)(−1−β)(−1−γ) or (α+1)(β+1)(γ+1)=−34 Also, αβγ=12∴ 4(α+1)(β+1)(γ+1)αβγ=−6

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