Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

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