Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.

Question

-1,3+i
f(x)=

Answer 1

complex roots always come in pairs which are conjugates of each other
so there are three roots, ...
-1, 3+i, and 3-i

f(x) = (x+1)(x - 3 - i)(x - 3 + i)
= (x+1)(x^2 -6x + 10)

If you have to expand it, do so.

Answer 2

Thanks