If - are the roots of the equationx3 - ax2 - bx - 2-0 such that - - -1- then the value of 2a - b will be -

Let nbsp;α, nbsp;β, nbsp;and nbsp;γ nbsp;be nbsp;roots nbsp;of nbsp;the nbsp;equationAx3 nbsp;+ nbsp;Bx2 nbsp;+ nbsp;Cx nbsp;+ nb ...

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Relation between Roots and Coefficients for Quadratic

If α,β,γ are ...

Question

If $α, β, γ$ are the roots of the equation $x^{3} + a x^{2} + b x + 2 = 0$ such that $α β$ = –1, then the value of 2a + b will be .

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Solution

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α, β, γ

x^{3} + a x^{2} + b x + 2 = 0

α β

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x^{3} + a x^{2} + b x + c = 0

(1 + α^{2}) (1 + β^{2}) (1 + γ^{2}) =

$I f α, β, γ a r e r o o t s e q u a t i o n x^{3} + a x^{2} + b x + c = 0, t h e n α^{- 1} + β^{- 1} + γ^{- 1} =$

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\frac{α}{α β + b} + \frac{β}{a α + b}

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B x^{2}

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