# algebraically closed

A field is *algebraically closed* if every polynomial with coefficients in the field has a root in the field.

Neither the field of rational numbers nor the field of real numbers is algebraically closed. For instance, the polynomial \(p(x)=x^2+2\) does not have a either a real or a rational root. However, it does have complex roots (\(\pm i \sqrt{2}\,\)), and indeed the field of complex numbers is algebraically closed.

- [MLA] “algebraically closed.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 21 Feb 2013. Web. 21 Feb 2013. <http://platonicrealms.com/> - [APA] algebraically closed (21 Feb 2013). Retrieved 21 Feb 2013 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/algebraically-closed/