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Math Help - find the field

  1. #1
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    find the field

    Find the field F and the polynomial f(x)=x^2+ax+b from F[x] with the derivation identically equal to 0, f(x) is not the second power of another polynomial.

    Can anybody give me a hint please?
    Thanks
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  2. #2
    MHF Contributor

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    Quote Originally Posted by sidi View Post
    Find the field F and the polynomial f(x)=x^2+ax+b from F[x] with the derivation identically equal to 0, f(x) is not the second power of another polynomial.

    Can anybody give me a hint please?
    Thanks
    such a field has to be an infinite field of characteristic 2 and we must also have a=0. here's an example that satisfies the conditions in your problem:

    Spoiler:
    F=\mathbb{F}_2(t), the field of rational functions over \mathbb{F}_2, and f(x)=x^2+t.
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