If alpha, beta, gamma are the roots of the eq | vedclass

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(D) The given equation is $x^3 + x + 1 = 0$.Comparing this with the standard cubic equation $ax^3 + bx^2 + cx + d = 0$,we have $a = 1, b = 0, c = 1, d

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$-1$

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(D) The given equation is $x^3 + x + 1 = 0$.Comparing this with the standard cubic equation $ax^3 + bx^2 + cx + d = 0$,we have $a = 1, b = 0, c = 1, d = 1$.According to the relationship between roots and coefficients,the product of the roots $\alpha \beta \gamma = -\frac{d}{a}$.Substituting the values,we get $\alpha \beta \gamma = -\frac{1}{1} = -1$.We need to find the value of $\alpha^3 \beta^3 \gamma^3$,which is equal to $(\alpha \beta \gamma)^3$.Therefore,$(\alpha \beta \gamma)^3 = (-1)^3 = -1$.

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:

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