I need help with this question please

Question

R has degree 4 and zeros 4 - 5i and 3, with 3 a zero of multiplicity 2.

Answer 1

Since 4 - 5i is a root then 4 + 5i is a root.

We are not given an extra point so we will just use a as the coefficient. (Or you can say that a = 1).

f(x) = a(x - 3)^2(x - 4 - 5i)(x - 4 + 5i)

f(x) = a(x^2 - 6x + 9)(x^2 - 8x + 41)

f(x) = a(x^4 - 14x^3 + 98x^2 - 318x + 369)