Question 668761
if -5 + 2i is a root of the polynomial f(x)
and f(x) has real coefficients then the conjugate must also be a root .

thus -5 - 2i is also a root.
it is also said that 2 is a root of multiplicity 2.


(x + 5 + 2i) (x + 5 - 2i) (x - 2)^2
= ((x + 5)^2 + 4) (x^2 - 4x + 4)
= (x^2 + 10x + 29) (x^2 - 4x + 4)
= x^4 + 6x^3 - 7x^2 - 76x + 116