My knowledge of polynomials is rather rusty, but given the fact that you found the values of m, you can substitute each value into the original equation and find the roots:
Starting with

:
One of the roots will be

, but according to the answer, it seems that we should disregard this, leaving us with:

i.e.

, matching the answer provided.
Moving on to

:
One of the roots will be

, but according to the answer, it seems that we should disregard this, leaving us with:

i.e.

, matching the answer provided.
There appears to be a different approach that would require the use of simultaneous equations, although I am not exactly sure as to how that would be performed.
I hope this helps!
