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Math Help - Algebraic Numbers

  1. #1
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    Algebraic Numbers

    A number r is algebraic if there is a nonzero polynomial p(x) with integer coefficients such that r is a root of p(x) = 0.

    Prove that every rational number is an algebraic number.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Algebraic Numbers

    Quote Originally Posted by thamathkid1729 View Post
    A number r is algebraic if there is a nonzero polynomial p(x) with integer coefficients such that r is a root of p(x) = 0.

    Prove that every rational number is an algebraic number.
    Let q be any rational number. q=a/b, where a and b are integers.

    bq-a=0

    bx-a is the nonzero polynomial p(x) with integer coefficients such that q is a root of p(x)=0.

    So, every rational number is an algebraic number.
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