Question

If $\alpha ,\beta$ and $\gamma$ are the zeroes of the polynomial $f\left(x\right)=a{x}^3+b{x}^2+cx+d$, then $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }$ is _____.

• A. $\frac{c}{d}$
• B. $\frac{a}{d}$
• C. $-\frac{c}{d}$
• D. $-\frac{b}{a}$

Answer 1

The correct option is C

$-\frac{c}{d}$

Given $\alpha ,\beta$ and $\gamma$ are the zeroes of the polynomial $f\left(x\right)=a{x}^3+b{x}^2+cx+d$

$\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }$

$=\frac{\beta \gamma +\alpha \gamma +\alpha \beta }{\left(\alpha \beta \gamma \right)}$ $=\frac{\left(\frac{c}{a}\right)}{(-\frac{d}{a})}$ $=-\frac{c}{d}$