Find a polynomial function having the following zeros:

Question

– 5, 3 (multiplicity 2), 2 + i, 2 – i; degree 5.

Answer 1

let's first do the quadratic which would give us roots of 2 ± i
(x - (2+i))(x - (2-i)) = .....
= x^2 - 4x + 5

so we have
f(x) = (x+5)(x-3)(x-3)(x^2 - 4x + 5)

which, if expanded will give us a 5th degree polynomial.