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Let $F$ be a field, and $p \in F[X]$ let be a polynomial of degree $n.$ There exists some field extension where $p$ has $n$ roots. Do you know the proof of following statement?


marked as duplicate by Thomas Shelby, André 3000, Lord Shark the Unknown abstract-algebra Feb 13 at 5:10

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  • $\begingroup$ its called the fundamental theorem of algebra. look it up $\endgroup$ – Seth Feb 13 at 0:35
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    $\begingroup$ This theorem works if $F$ is field of complex numbers, not all fields. $\endgroup$ – benjamin1996 Feb 13 at 0:42
  • $\begingroup$ I was looking at this just yesterday but realised it's beyond what I know so gave up $\endgroup$ – Displayname Feb 13 at 0:49