Dictionary

rational root theorem en · PROPN

Meanings

1. A theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.
   • The 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 85:
   • We 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 84:
   • 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.
   • 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+7

Forms

Synonyms

p/q theorem · rational root test · rational zeros test · rational zeros theorem

Translations (15)

gl teorema das raíces racionais (theorem in algebra) · gl teorema dos ceros racionais (theorem in algebra) · fr théorème de la racine rationnelle (theorem in algebra) · pt teorema do zero racional (theorem in algebra) · pt teorema das raízes racionais (theorem in algebra) · it teorema delle radici razionali (theorem in algebra) · fi rationaalijuuritesti (theorem in algebra) · es teorema de las raíces racionales (theorem in algebra) · fi rationaalijuurilause (theorem in algebra) · fr théorème des racines rationnelles (theorem in algebra) · ca teorema de les arrels racionals (theorem in algebra) · es teorema de los ceros racionales (theorem in algebra) · es teorema de la raíz racional (theorem in algebra) · de Satz über rationale Nullstellen (theorem in algebra) · fr théorème du zéro rationnel (theorem in algebra)