# Article

# Article

- Mathematics
- Algebra and number theory
- Theory of equations

# Theory of equations

Article By:

**Beaumont, Ross A. **Formerly, Department of Mathematics, University of Washington, Seattle, Washington.

Last reviewed:January 2021

DOI:https://doi.org/10.1036/1097-8542.239300

**The branch of mathematics concerned with finding facts concerning the roots of algebraic equations and finding methods for obtaining them.** The most important type of algebraic equation is the polynomial equation in one unknown which is an expression of the form *f* (*x*) = *a*_{n} *x*^{n} + *a*_{n−1} *x*^{n−1} + + *a*_{1} *x* + *a*_{0} = 0, where *x* is called the unknown, or variable; *n* is a positive whole number; and the *a*_{i}, with *i* = 0, 1, …, *n*, are constants, or fixed numbers, called coefficients of the equation. The left member of the equation is called a polynomial in one variable of degree *n*. A root of such an equation is a number which, when substituted for the variable *x*, makes the left member zero. For example, 3 is a root of the equation *x*^{3} + 2*x*^{2} − 13*x* − 6 = 0. In addition, systems of equations in one or more variables are considered, and here the problem is to find values for the variables which simultaneously satisfy each equation of the system.* See also: ***Linear systems of equations**; **Polynomial systems of equations**

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