If $\alpha, \beta$ and $\gamma$ are the root of the equation $x^3-6 x^2+11 x+6=0$, then $\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2$ is equal to

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Aicharya · Accepted Answer

$\alpha, \beta$ and $\gamma$ are roots of $x^3-6 x^2+11 x+6=0$ Then, $\alpha+\beta+\gamma=6, \alpha \beta+\beta \gamma+\gamma \alpha=11$ and $\alpha \beta \gamma=-6$ Now, $ \begin{aligned} \Sigma \alpha^2 \beta+ & \Sigma \alpha \beta^2 \ & =(\alpha+\beta+\gamma)(\alpha \beta+\beta \gamma+\gamma \alpha)-3 \alpha \beta \gamma \ & =(6)(11)-3(-6)=66+18=84 \end{aligned} $

If $\alpha, \beta$ and $\gamma$ are the root of the equation $x^3-6 x^2+11 x+6=0$, then $\Sigma \alpha^2…

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