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  • If are the zeroes of the polynomial <img alt="p(x)=a x^{3}+b x^{2}+

If \alpha, \beta, \gamma are the zeroes of the polynomial p(x)=a x^{3}+b x^{2}+c x +\mathrm{d}, then find the value of \frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma} is

Option: 1

-c/d


Option: 2

b/d


Option: 3

-a/d


Option: 4

a/d


Answers (1)

best_answer

\text { Let } p=\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma} \Rightarrow p=\frac{\beta \gamma+\gamma \alpha+\alpha \beta}{\alpha \beta \gamma}

Since, 

\alpha \beta \gamma=-\mathrm{d} / \mathrm{a}

and

\alpha \beta+\beta \gamma+\gamma \alpha=c / a

 

\Rightarrow p=\frac{c / a}{-d / a}=-\frac{c}{d}

 

Posted by

himanshu.meshram

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