roots of minimal polynomial in a simple field extension.

Hi,

Let be a field and let be a simple field extension of . Let be the minimal polynomial of over .

My question is how many roots does have in ?

Clearly, by definition we have that . So we at least have one roots (namely ) but i've got a feeling this is actually the only roots. Is that correct?

Thanks for any help!

Re: roots of minimal polynomial in a simple field extension.

Quote:

Originally Posted by

**Ant** Hi,

Let

be a field and let

be a simple field extension of

. Let

be the minimal polynomial of

over

.

My question is how many roots does

have in

?

Clearly, by definition we have that

. So we at least have one roots (namely

) but i've got a feeling this is actually the only roots. Is that correct?

Thanks for any help!

You mean "this is **not** actually the only root", right?