Find a polynomial with integer coefficients that satisfies the given conditions.

Question

P has degree 2 and zeros

2 + i and 2 − i.

Answer 1

clearly, one such

P(x) = (x-(2+i))(x-(2-i))
= ((x-2)-i)((x-2)+i)
= (x-2)^2 - i^2
= x^2-4x+4 + 1
= x^2-4x+5

extra credit: why does the question imply that there is more than one such P(x)?