Question

If $\alpha ,\beta$ and $\gamma$ are the roots of the cubic equation $3x^3+2x^2+x-1=0$, then the value of $(\alpha \beta +\beta \gamma +\gamma \alpha )$ is:

• A. $3$
• B. $2$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

The correct option is D $\frac{1}{3}$

Given $\alpha ,\beta ,\gamma$ are the roots of the equation $3x^3+2x^2+x-1=0$
Comparing with $a{x}^3+b{x}^2+cx+d=0$ , we get $a=3,b=2,c=1,d=-1$
So, $\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a}=\frac{1}{3}$