If alpha , beta , gamma are roots of equatio | vedclass

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Question

(b) $\alpha , \beta , \gamma $ are the roots of the equation

${x^3} + a{x^2} + bx + c = 0$

so $\alpha + \beta + \gamma = - a$, $\alpha \beta + \

Vedclass · Accepted Answer

$-b/c$

Vedclass · Answer

(b) $\alpha , \beta , \gamma $ are the roots of the equation

${x^3} + a{x^2} + bx + c = 0$

so $\alpha + \beta + \gamma = - a$, $\alpha \beta + \beta \gamma + \gamma \alpha =b$ and $\alpha \beta \gamma = - \,c$

Now ${\alpha ^{ - 1}} + {\beta ^{ - 1}} + {\gamma ^{ - 1}}$ $ = \frac{1}{\alpha } + \frac{1}{\beta } + \frac{1}{\gamma }$ $ = \frac{{\alpha \beta + \beta \gamma + \gamma \alpha }}{{\alpha \beta \gamma }}= - b/c$.

If $\alpha , \beta , \gamma $ are roots of equation ${x^3} + a{x^2} + bx + c = 0$, then ${\alpha ^{ - 1}} + {\beta ^{ - 1}} + {\gamma ^{ - 1}} = $

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