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
![](https://latex.codecogs.com/png.latex?\bg_white m=-12)
:
One of the roots will be
![](https://latex.codecogs.com/png.latex?\bg_white x=-4)
, but according to the answer, it seems that we should disregard this, leaving us with:
![](https://latex.codecogs.com/png.latex?\bg_white x=1+\sqrt5\:,\:x=1-\sqrt5)
i.e.
![](https://latex.codecogs.com/png.latex?\bg_white x=1\pm \sqrt{5})
, matching the answer provided.
Moving on to
![](https://latex.codecogs.com/png.latex?\bg_white m=-20)
:
One of the roots will be
![](https://latex.codecogs.com/png.latex?\bg_white x=4)
, but according to the answer, it seems that we should disregard this, leaving us with:
![](https://latex.codecogs.com/png.latex?\bg_white x=-3+\sqrt5\:,\:x=-3-\sqrt5)
i.e.
![](https://latex.codecogs.com/png.latex?\bg_white x=-3\pm \sqrt5)
, 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!
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