If α,β,γ are the roots of x3 + qx + r = 0 then Σ(β+γ)−1=

α+β+γ=0⇒β+γ=−α;Σ(β+γ)−1=−1α+1β+1γ=−(αβ+βγ+γα)αβγ=−q−r=qr

If α,β,γ are the roots of x3 + qx + r = 0 then Σ(β+γ)−1=

α+β+γ=0⇒β+γ=−α;Σ(β+γ)−1=−1α+1β+1γ=−(αβ+βγ+γα)αβγ=−q−r=qr

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If $α, β, γ$ are the roots of x³ + qx + r = 0 then $Σ (β + γ)^{- 1} =$

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q/r

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-r/q

answer is A.

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$\begin{array}{l} α + β + γ = 0 \Rightarrow β + γ = - α; \\ Σ (β + γ)^{- 1} = - (\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}) \\ = - \frac{(αβ + βγ + γα)}{αβγ} = \frac{- q}{- r} = \frac{q}{r} \end{array}$

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If $α, β, γ$ are the roots of x³ + qx + r = 0 then $Σ (β + γ)^{- 1} =$