Finding real coefficients of polynomial with complex roots I have been tasked with finding the just real coefficients of a polynomial with the roots:
$z_{0}=10$
$z_{1}=3-i$
$z_{2}=-8+2i$
Writing the polynomial as factors...
$(z-10)(z-3+i)(z+8-2i)$
..obviously does not work since this results in complex coefficients.
Can anyone help me out here?

There is not enough information, say the degree of a given polynomial. 
Anyway, since it has (only) real coeficients if $a+bi$ is one root, then $a-bi$ is also a root of the polynomial.
So this polynomial is divisible with: 
$$q(z)=(z-10)\color{red}{(z-3+i)(z-3-i)}\color{blue}{(z+8-2i)(z+8+2i)} $$
$$= (z-10)(z^2-6z+10)(z^2+16z+68)$$
