Question

write, in extended form, a polynomial(with real coefficients) of degree 3, with solutions 2,2-i.

Answer 1

complex roots always come in pairs, so if 2-i is a root, so is 2+i
using the sum and product of roots property of a quadratic,
sum of roots = 2-1 + 2+i = 4
product or roots = (2-i)(2+i) = 4 - i^2 = 5
so the quadratic part would be
x^2 - 4x + 5
the other factor would be x-2

so the polynomial is
(x-2)(x^2 - 4x + 5)

I will leave it up to you to expand it, if you need it in that form.