Question

f(x) is a polynomial function of degree 4 whose coefficients are real numbers three of its zeros are 2, 1+2i, and 1-2i. Explain why the remaining zero must be a real number.

Answer 1

cause every imaginary zero already has a complex conjugate which is also a zero of the function. Therefore, that pair is already completed. so you're down to 2 zero. Since one of them is a real zero, the last one can't be imaginary.