Write a polynomial equation with integral coefficients that has 1/2 and 2i as solutions

Answer 1

since we have real coefficients, and 2i is a root, so is -2i. If 1/2 is a root, one factor of p(x) is (2x-1). So,

p(x) = (2x-1)(x-2i)(x+2i)
= (2x-1)(x^2+4)