# Number of roots and degree of polynomial [duplicate]

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 StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 13 at 5:10

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