Write a polynomial function of least degree with integral coefficients that has the following zeros: -2, and 2-i

Answer 1

To ensure real coefficients, the complex conjugate of any complex zero must also be a zero. Therefore you must have at least 3 zeros:

-2

2 - i

2 + i

f(x) = A(x + 2) [x - (2 - i)] [x - (2 + i)]

with A real, integer, and A ≠ 0. You can expand f(x) to standard form if you wish. The coefficients will come out real.