Question

The value of $m$ for which one root of the quadratic equation $x^2-3x+2m=0$ is twice the other is

Answer 1

Let the roots of the quadratic equation $x^2-3x+2m=0$ are $\alpha ,2\alpha$
where $a=1,b=-3,c=2m$ and $k=2$
$\Rightarrow \frac{b^2}{ac}=\frac{(k+1{)}^2}{k}$
$\Rightarrow \frac{(-3{)}^2}{1\times 2m}=\frac{(2+1{)}^2}{2}$
$\Rightarrow m=1$

Alternate Solution:
$\alpha +2\alpha =3$
$\Rightarrow \alpha =1$
$\alpha \times 2\alpha =2m$
$\Rightarrow m=1$