Question

Find a second degree polynomial with integer coefficients that has (2+i) as one of its zeros and whose constant term is 5.

Answer 1

we are given one zero as 2+i so the other zero would be 2-i
as complex roots always occur in conjugate pairs
(x-(2+i))(x-(2+i))=0
x^2-x(2+i)-x(2-i)+(4-i^2)=0
i^2=-1
x^2-4x+5=0