Suppose that E is a field extension of F, and every polynomial f(x) in F[x] has a root in E. Then E is algebraically closed, i.e. every polynomial f(x) in E[x] has a root in E.(adsbygoogle = window.adsbygoogle || []).push({});

I've been told that this result is really difficult to prove, but it seems really intuitive so I find that surprising. Where can I find a proof of this result?

Any help would be greatly appreciated.

Thank You in Advance.

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# How to prove the field extension is algebraically closed

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