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(C) Given the quadratic equation $x^2 + ax + b = 0$.By the relation between roots and coefficients,the sum of roots $\alpha + \beta = -a$ and the prod

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$- a^3 + 3ab$

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(C) Given the quadratic equation $x^2 + ax + b = 0$.By the relation between roots and coefficients,the sum of roots $\alpha + \beta = -a$ and the product of roots $\alpha \beta = b$.We know the algebraic identity $\alpha^3 + \beta^3 = (\alpha + \beta)(\alpha^2 - \alpha \beta + \beta^2)$.This can be rewritten as $\alpha^3 + \beta^3 = (\alpha + \beta)[(\alpha + \beta)^2 - 3\alpha \beta]$.Substituting the values,we get $\alpha^3 + \beta^3 = (-a)[(-a)^2 - 3(b)]$.$\alpha^3 + \beta^3 = (-a)(a^2 - 3b) = -a^3 + 3ab$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + ax + b = 0$,then the value of $\alpha^3 + \beta^3$ is equal to:

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