rational root theorem

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English

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Proper noun

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rational root theorem

  1. (algebra) A theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.
    Synonyms: rational root test, rational zero theorem, rational zero test, p/q theorem
    The rational root theorem states that if the rational number is a root of the polynomial equation , with , then and .
    • 2015, Marlow Anderson, Todd Feil, A First Course in Abstract Algebra, Taylor & Francis (CRC Press), 3rd Edition, page 50,
      Use the Rational Root Theorem 5.6 to argue that
      is irreducible over .
    • 2017, Martin H. Weissman, An Illustrated Theory of Numbers, American Mathematical Society, page 84:
      We demonstrate how to use the rational root theorem to prove the irrationality of many numbers.
    • 2018, Mary Jane Sterling, Pre-Calculus For Dummies, Wiley, page 85:
      The rational root theorem has you create a list of possible rational roots using the lead coefficient and constant in the polynomial equation.

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Further reading

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