Question

Given that 1 − 2i is a root of
z4 + 11z2 − 10z + 50 = 0
find the other roots.

Answer 1

we know that 1+2i is also a root since the coefficients of the polynomial are real. Therefore z^4 + 11z^2 - 10^z +50 = (z^2 - 2z + 5)(Az^2 + Bz +C)
By inspection (comparing coefficients) we find A = 1, B = 2, C = 10
therefore solving the equation: (z^2 - 2z + 5)(z^2 - 2z + 10) = 0 is the same as solving z^4 + 11z^2 - 10^z +50 = 0. Im sure you will be able to get the final answer from here