Question

If $\Sigma \alpha =\frac{2}{3},\Sigma \alpha \beta =\frac{4}{3}$ and $\alpha \beta \gamma =\frac{8}{3}$, then the equation whose roots are $\alpha ,\beta ,\gamma$, is

• A. $x^3-2x^2+4x-8=0$
• B. $3x^3+2x^2-4x+8=0$
• C. $3x^3-2x^2+4x-8=0$
• D. $x^3+2x^2-4x+8=0$

Answer 1

Answer: (C)

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

The equation with roots $\alpha ,\beta ,\gamma$ is given by,
$x^3-(\sum \alpha )x^2+(\sum \alpha \beta )x-\alpha \beta \gamma =0$
$\Rightarrow x^3-\frac{2}{3}{x}^2+\frac{4}{3}x-\frac{8}{3}=0$
$\Rightarrow 3x^3-2x^2+4x-8=0$