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If $α, β, γ$ are the roots of $x^{3} + x^{2} + 2 x + 3 = 0$ then the equation whose roots $β + γ,$ $γ + α, α + β$ is

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$x^{3} + 2 x^{2} + 3 x - 1 = 0$

$x^{3} + 2 x^{2} + 3 x + 1 = 0$

$x^{3} + 2 x^{2} - 3 x - 1 = 0$

$x^{3} - 2 x^{2} + 3 x - 1 = 0$

answer is A.

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Detailed Solution

let $α + β = y$

$(\sin c e α + β + γ = - 1)$

$γ = - 1 - y$

since $γ i s a r o o t o f g i v e n e q u a t i o n \Rightarrow$

$f (- 1 - y) = 0$

$\Rightarrow y^{3} + 2 y^{2} + 3 y - 1 = 0$

$\Rightarrow x^{3} + 2 x^{2} + 3 x - 1 = 0$

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