If $\alpha,\beta,\gamma$ are the roots of the equation $x^{3} + x + 1 = 0$, then the value of $\alpha^{3} + \beta^{3} + \gamma^{3}$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Here, $\alpha + \beta + \gamma = 0,\ \ \alpha\beta + \beta\gamma + \gamma\alpha = 1$
And $\alpha\beta\gamma = - 1$
$	herefore\ \alpha^{3} + \beta^{3} + \gamma^{3}$
$= (\alpha + \beta + \gamma)\left\lbrack \alpha^{2} + \beta^{2} + \gamma^{2} - \alpha\beta - \beta\gamma - \gamma\alpha ightbrack + 3\alpha\beta\gamma$
$= 0 + 3( - 1) = - 3$

Q. If $\alpha,\beta,\gamma$ are the roots of the equation $x^{3} + x + 1 = 0$, then the value of $\alpha^{3} + \beta^{3} + \gamma^{3}$ is

Explanation

Reviewed by Dr. Abubacker

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