$Thevalueofmforwhichoneoftherootsof{x}^2-3x+2m=0istwotimesarootof{x}^2-x+m=0is$

$\begin{array}{l}Let\alpha isrootof{x}^2-x+m=0\Rightarrow {\alpha }^2-\alpha +m=0--\left(1\right)\\ and2\alpha isrootof{x}^2-3x+2m=0\Rightarrow 4{\alpha }^2-b\alpha +2m=0--\left(2\right)\\ solving\left(1\right)\&\left(2\right)\\ {\alpha }^2\alpha 1\\ \begin{array}{cccc}-1& m& 1& -1\\ -6& 2m& 4& -6\end{array}\\ \Rightarrow \frac{{\alpha }^2}{-2m+6m}=\frac{\alpha }{4m-2m}=\frac{1}{-6+4}\\ \Rightarrow \frac{{\alpha }^2}{4m}=\frac{\alpha }{2m}=\frac{1}{-2}\\ \Rightarrow {\alpha }^2=-2m,\Rightarrow \alpha =m\\ \Rightarrow m^2=-2m\\ \Rightarrow m^2+2m=0\Rightarrow m(m+2)=0\\ \therefore m=0,-2\end{array}$