List all solutions if x^4 + x^3 - 11x^2 + 9x + 20 = 0 and if one of the roots is x = (2+i)
if one root is 2 + i, then another is 2 - i, since complex roots always come in conjugates.
thus we can write:
where are the remaining 2 roots, they may be another complex conjugate pair or real (i think they are real though).
expand the right side and equate the coefficients to solve for and
OR you can do it the long way and try to find real roots of the equation by plugging in factors of 20 and doing the necessary long divisions. that may work
EDIT: Yup, looked at it, still don't get it
EDIT: Oh wait, i think i found something (in particular, see theorem 5): General theorems for polynomials
now to just figure out a way to memorize it