Definitions for algebraic equation
al·ge·bra·ic equa·tion

WiktionaryRate this definition:1.0 / 2 votes

1. algebraic equationnoun

   A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3.

WikipediaRate this definition:0.0 / 0 votes

1. Algebraic equation

   In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the multivariate case), the term polynomial equation is usually preferred to algebraic equation. For example, x 5 − 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0} is an algebraic equation with integer coefficients and y 4 + x y 2 − x 3 3 + x y 2 + y 2 + 1 7 = 0 {\displaystyle y^{4}+{\frac {xy}{2}}-{\frac {x^{3}}{3}}+xy^{2}+y^{2}+{\frac {1}{7}}=0} is a multivariate polynomial equation over the rationals. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only those same types of coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or four; but for degree five or more it can only be done for some equations, not all. A large amount of research has been devoted to compute efficiently accurate approximations of the real or complex solutions of a univariate algebraic equation (see Root-finding algorithm) and of the common solutions of several multivariate polynomial equations (see System of polynomial equations).

WikidataRate this definition:0.0 / 0 votes

1. Algebraic equation

   In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers. For most authors, an algebraic equation is univariate, which means that it involves only one variable. On the other hand, a polynomial equation may involve several variables, in which case it is called multivariate and the term polynomial equation is usually preferred to algebraic equation. For example, is an algebraic equation with integer coefficients and is a polynomial equation over the rationals. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression with a finite number of operations involving just those coefficients. This can be done for all such equations of degree one, two, three, or four; but for degree five or more it can only be done for some equations but not for all. A large amount of research has been devoted to compute efficiently accurate approximations of the real or complex solutions of an univariate algebraic equation and of the common solutions of several multivariate polynomial equations.

How to pronounce algebraic equation?

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Numerology

1. Chaldean Numerology

   The numerical value of algebraic equation in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of algebraic equation in Pythagorean Numerology is: 7

Examples of algebraic equation in a Sentence

1. Eric Butterworth:

   In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Algebraic_Equation
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Algebraic_Equation
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=algebraic equation