Theory of equations
Beaumont, Ross A. Formerly, Department of Mathematics, University of Washington, Seattle, Washington.
Last reviewed:January 2021
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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) = an xn + an−1 xn−1 + + a1 x + a0 = 0, where x is called the unknown, or variable; n is a positive whole number; and the ai, 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 x3 + 2x2 − 13x − 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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