How do you find a third degree polynomial given roots #5# and #2i#?
Please see the explanation section below.
For a third degree polynomial, we need 3 linear factors.
If we want a polynomial with real coeficients, then the complex conjugate of
One polynomial with real coefficients that meets the requirements is
# = x^3-5x^2+4x-20#
Any constant multiple of this also meets the requirements.