Problem - 2592
If one root of the equation $x^2 -6x+m^2-2m+5=0$ is $2$. Find the value of the other root and $m$.
By the Vieta's theorem, the sum of these two roots are 6. Hence the other root is $\boxed{4}$.
Applying the Vieta's theorem again yields
$$2\times 4 = m^2-2m+5 \implies m= \boxed{3, -1}$$