If $P(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_1z+a_o$ a polynomial who's coefficients are all real.
Explain why if $z_1$ is a root of $P$, then $\bar{z_1}$ is also a root.
And give an example as to why the contrary is false if the coefficients of $P$ are not all real.