Question

Let $\alpha$ and $\beta$ be the roots of the equation $3x^2-6x+5=0$ then the equation whose roots are $(\alpha +\beta )$ and $\frac{2}{(\alpha +\beta )}$ is

• A. $x^2+3x-1=0$
• B. $x^2+3x-2=0$
• C. $x^2-3x+2=0$
• D. $x^2-3x-2=0$

Answer 1

The correct option is C $x^2-3x+2=0$

$\alpha$ & $\beta$ are roots of equation
$3x^2-6x+5=0$
$x^2-\frac{6}{3}x+\frac{5}{3}=0$
$x^2-2x+\frac{5}{3}=0$
So, $\alpha +\beta =2$ & $\alpha \beta =\frac{5}{3}$
Equation whose roots are $(\alpha +\beta )$ & $\frac{2}{(\alpha +\beta )}$
$=x^2-[(\alpha +\beta )+\frac{2}{(\alpha +\beta )}]x+\frac{(\alpha +\beta )}{(\alpha +\beta )}=0$
$=x^2-(2+\frac{2}{2})x+2=0$
$=x^2-3x+2=0$