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If α, β, ...

Question

If $α$ , $β$ , $γ$ are the roots of $x^{3} - x^{2} + 8 x + 6 = 0$ the $(1 + α) (1 + β) (1 + γ) =$

A

4

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B

12

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C

14

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D

24

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Solution

The correct option is A $4$
$x^{3} - x^{2} + 8 x + 6 = 0$
Roots are $α, β, γ$
$α + β + γ = 1$
$α β + β γ + γ α = 8$
$α β γ = - 6$
$(1 + α) (1 + β) (1 + γ) = (1 + α + β + α β) (1 + γ)$
$= 1 + α + β + γ + α β + β γ + γ α + α β γ$
$= 1 + 1 + 8 - 6$
$= 4$

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