Please help!! I do not understand any of this!!

Question

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree 4; zeros: 8,-6-i

Answer 1

you know this much..

(x-8)(x+6+i) and coefficents with real numbers adds the complex conjugate
(x-8)(x+6+i)(x+6-i) that is degree three.

so to get any fourth degree equation with those roots, you can add any other root, or make the root at 8 a double root such as
f(x)=(x-8)^2 * (x+6+i)(x+6-i)