If alpha ,beta and gamma are the roots of { | vedclass

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Question

(a) We have, ${x^3} + px + q = 0$ .....$(i)$

$	herefore $ The roots of equation $(i)$ is $\alpha ,\,\beta $ and $\gamma $

$	herefore $ The sum

Vedclass · Accepted Answer

$ - 3q$

Vedclass · Answer

(a) We have, ${x^3} + px + q = 0$ .....$(i)$

$	herefore $ The roots of equation $(i)$ is $\alpha ,\,\beta $ and $\gamma $

$	herefore $ The sum of roots = $\alpha + \beta + \gamma $

= $\frac{{{m{Coefficient of }}{x^2}}}{{{m{Coefficient of }}{x^3}}} = \frac{{ - 0}}{1} = 0$

and the product of any two roots

= $\alpha \beta + \beta \gamma + \gamma \alpha = \frac{{{m{Coefficient of }}x}}{{{m{Coefficient of }}{x^3}}} = p$

$	herefore $ Product of all three roots = $\alpha \beta \gamma $= ${t_1} = (d/{v_1})$

$\alpha + \beta + \gamma = 0$

$	herefore $ ${\alpha ^3} + {\beta ^3} + {\gamma ^3} = 3\alpha \beta \gamma = - 3q$.

If $\alpha ,\beta $ and $\gamma $ are the roots of ${x^3} + px + q = 0$, then the value of ${\alpha ^3} + {\beta ^3} + {\gamma ^3}$ is equal to

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