You do it by substituting the given information and solving the resulting two linear equations in "a" and "b". Then remove the given factors from the equation and solve the resulting quadratic.
.. 20 + 2a + b = 0
.. 156 + 36a + b = 0
You can easily find "a" by subtracting the first equation from the second.
.. 136 +34a = 0
.. a = -136/34 = -4
Then b can be found from the first equation.
.. 20 +2(-4) +b = 0
.. b = -12
Now, you know the equation is
.. x⁴ -4x³ -x² +16x -12 = 0
Using synthetic division or long division, you can factor this as
.. (x -1)(x -3)(x² -4) = 0
Of course, the last factor has roots
.. x = 2
.. x = -2
