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Math Help - roots of minimal polynomial in a simple field extension.

  1. #1
    Ant
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    roots of minimal polynomial in a simple field extension.

    Hi,

    Let K be a field and let L=K[l] be a simple field extension of K. Let m_{K,l} be the minimal polynomial of  l over K.

    My question is how many roots does m_{K,l} have in  L?

    Clearly, by definition we have that m_{K,l}(l)=0. So we at least have one roots (namely  l ) but i've got a feeling this is actually the only roots. Is that correct?

    Thanks for any help!
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  2. #2
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    Re: roots of minimal polynomial in a simple field extension.

    Quote Originally Posted by Ant View Post
    Hi,

    Let K be a field and let L=K[l] be a simple field extension of K. Let m_{K,l} be the minimal polynomial of  l over K.

    My question is how many roots does m_{K,l} have in  L?

    Clearly, by definition we have that m_{K,l}(l)=0. So we at least have one roots (namely  l ) 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?
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