Let P ∈ R [ X ] {\displaystyle {}P\in \mathbb {R} [X]} be a polynomial with real coefficients and let z ∈ C {\displaystyle {}z\in \mathbb {C} } be a root of P {\displaystyle {}P} . Show that also the complex conjugate z ¯ {\displaystyle {}{\overline {z}}} is a root of P {\displaystyle {}P} .
![{\displaystyle {}P\in \mathbb {R} [X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9bf6bcf64e16c3ac6b30ecd6577e72648ab2325a)
