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Math Help - algebraic numbers

  1. #1
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    algebraic numbers

    x is algebraic and let y = x + 3. Is y algebraic? and why is it?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: algebraic numbers

    Quote Originally Posted by thomasboateng View Post
    x is algebraic and let y = x + 3. Is y algebraic? and why is it?
    Let f(x) be the irreducible polynomial for x over F. Then, the irreducible polynomial for y over F is f(y-3). So, y is algebraic.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: algebraic numbers

    More general, \mathbb{A}=\{x\in\mathbb{R}:\; x\mbox{ & algebraic & over}\;\mathbb{Q}\} is a field (non finite extension of \mathbb{Q})
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