If $\alpha, \beta, \gamma$ are roots of the equation $x^3+a x^2+b x+c=0$ then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}=$

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Aicharya · Accepted Answer

Given $\alpha, \beta, \gamma$ are roots of $x^3+a x^2+b x+c=0$ So, $\alpha \cdot \beta \cdot \gamma=\frac{-c}{a}$ and $\alpha \beta+\beta \gamma+\alpha \gamma=\frac{b}{a}$ Now, $\alpha^{-1}+\beta^{-1}+\gamma^{-1}=\frac{\alpha \beta+\beta \gamma+\alpha \gamma}{\alpha \beta \gamma}=\frac{-b}{c}$.

If $\alpha, \beta, \gamma$ are roots of the equation $x^3+a x^2+b x+c=0$ then…

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