See rational root theorem in All languages combined, or Wiktionary
Download JSON data for rational root theorem meaning in English (2.6kB)
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"text": "The rational root theorem states that if the rational number p#x2F;q is a root of the polynomial equation a#x5F;nxⁿ#x2B;a#x5F;#x7B;n-1#x7D;x#x7B;n-1#x7D;#x2B;#x5C;cdots#x2B;a#x5F;0#x3D;0, with a#x5F;0,#x5C;ldotsa#x5F;n#x5C;in#x5C;mathbb#x7B;Z#x7D;, then p#x5C;verta#x5F;0 and q#x5C;verta#x5F;n.",
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"ref": "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 x³+x+7",
"text": "is irreducible over Q [x]."
},
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"ref": "2017, Martin H. Weissman, An Illustrated Theory of Numbers, American Mathematical Society, page 84",
"text": "We demonstrate how to use the rational root theorem to prove the irrationality of many numbers.",
"type": "quotation"
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"ref": "2018, Mary Jane Sterling, Pre-Calculus For Dummies, Wiley, page 85",
"text": "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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"A theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients."
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"(algebra) A theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients."
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"word": "rational root test"
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"word": "rational zero theorem"
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"word": "Satz über rationale Nullstellen"
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"sense": "theorem in algebra",
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"word": "teorema delle radici razionali"
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"text": "The rational root theorem states that if the rational number p#x2F;q is a root of the polynomial equation a#x5F;nxⁿ#x2B;a#x5F;#x7B;n-1#x7D;x#x7B;n-1#x7D;#x2B;#x5C;cdots#x2B;a#x5F;0#x3D;0, with a#x5F;0,#x5C;ldotsa#x5F;n#x5C;in#x5C;mathbb#x7B;Z#x7D;, then p#x5C;verta#x5F;0 and q#x5C;verta#x5F;n.",
"type": "example"
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"ref": "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 x³+x+7",
"text": "is irreducible over Q [x]."
},
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"ref": "2017, Martin H. Weissman, An Illustrated Theory of Numbers, American Mathematical Society, page 84",
"text": "We demonstrate how to use the rational root theorem to prove the irrationality of many numbers.",
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"ref": "2018, Mary Jane Sterling, Pre-Calculus For Dummies, Wiley, page 85",
"text": "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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