\overline{P(z)}=\overline{a_n z^n + a_{n-1} z^{n-1} + ... + a_1 z + a_0} = 0 = P(z)=a_n \overline{z}^n + a_{n-1} \overline{z}^{n-1} + ... + a_1 \overline{z} + a_0 = P(\overline{z})