Question

lf $\alpha ,\beta ,\gamma ,\delta$ are the roots of the equation $3x^4-8x^3+2x^2-9=0$, then $\Sigma \alpha \beta =$

• A. $\frac{2}{3}$
• B. $\frac{-2}{3}$
• C. $\frac{8}{3}$
• D. $\frac{-8}{3}$

Answer 1

The correct option is A $\frac{2}{3}$

Consider the given equation

$3x^4-8x^3+2x^2-9=0$

We know that
For equation $A{x}^4+B{x}^3+C{x}^2+Dx+E=0$

$\alpha \beta +\beta \gamma +\gamma \delta +\delta \alpha =\frac{C}{A}$

Here $C=2$ and $A=3$

Hence, $\sum \alpha \beta =\frac{C}{A}=\frac{2}{3}$.