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# algebraic equation

The equation

$f(x_{1},\,x_{2},\,...,\,x_{m})=0,$ |

where the left hand side is a polynomial in $x_{1}$, $x_{2}$, …, $x_{m}$ with coefficients in a certain field, is called an algebraic equation over that field. Often the field in question is $\mathbb{Q}$; then the coefficients may be assumed to be integers.

By the degree of an algebraic equation is meant the degree of the polynomial.

E.g. $3x^{2}-1=0$ and $x^{3}+x^{2}y+xy^{2}+y^{3}=0$ are algebraic equations over the field $\mathbb{Q}$, the degrees of which are 2 and 3.

Defines:

degree of equation

Related:

Equation, PolynomialEquationOfOddDegree, SymmetricQuarticEquation

Major Section:

Reference

Type of Math Object:

Definition

Parent:

## Mathematics Subject Classification

13P05*no label found*11C08

*no label found*12E05

*no label found*

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