Meanings
- algebraA theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.
The rational root theorem states that if the rational number p#47;q is a root of the polynomial equation a#95;nxⁿ#43;a#95;#123;n-1#125;x#123;n-1#125;#43;#92;cdots#43;a#95;0#61;0, with a#95;0,#92;ldotsa#95;n#92;in#92;mathbb#123;Z#125;, then p#92;verta#95;0 and q#92;verta#95;n.
3 more examples
is irreducible over Q [x].
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+7We demonstrate how to use the rational root theorem to prove the irrationality of many numbers.
2017, Martin H. Weissman, An Illustrated Theory of Numbers, American Mathematical Society, page 84The rational root theorem has you create a list of possible rational roots using the lead coefficient and constant in the polynomial equation.
2018, Mary Jane Sterling, Pre-Calculus For Dummies, Wiley, page 85Synonyms: rational root test, rational zeros theorem, rational zeros test, p/q theorem
Synonyms & antonyms
proper nounA theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.
Translations
Catalan teorema de les arrels racionals
- teorema de les arrels racionalstheorem in algebra
Finnish rationaalijuurilause, rationaalijuuritesti
- rationaalijuurilausetheorem in algebra
- rationaalijuuritestitheorem in algebra
French théorème des racines rationnelles, théorème de la racine rationnelle
- théorème des racines rationnellestheorem in algebra
- théorème de la racine rationnelletheorem in algebra
- théorème du zéro rationneltheorem in algebra
German Satz über rationale Nullstellen
- Satz über rationale Nullstellentheorem in algebra
Italian teorema delle radici razionali
- teorema delle radici razionalitheorem in algebra
Portuguese teorema do zero racional, teorema das raízes racionais
- teorema do zero racionaltheorem in algebra
- teorema das raízes racionaistheorem in algebra
Spanish teorema de los ceros racionales, teorema de la raíz racional
- teorema de los ceros racionalestheorem in algebra
- teorema de la raíz racionaltheorem in algebra
- teorema de las raíces racionalestheorem in algebra
Cite this entry
rational root theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/rational%20root%20theorem
“rational root theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/rational%20root%20theorem. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “rational root theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/rational%20root%20theorem.
Source: rational root theorem on Wiktionary, CC BY-SA 4.0.