algebraic equation

Math.an equation in the form of a polynomial having a finite number of terms and equated to zero, as 2x^{3} + 4x^{2}  x + 7 = 0.
* * *
Mathematical statement of equality between algebraic expressions.An expression is algebraic if it involves a finite combination of numbers and variables and algebraic operations (addition, subtraction, multiplication, division, raising to a power, and extracting a root). Two important types of such equations are linear equations, in the form y = ax + b, and quadratic equations, in the form y = ax^{2} + bx + c. A solution is a numerical value that makes the equation a true statement when substituted for a variable. In some cases it may be found using a formula; in others the equation may be rewritten in simpler form. Algebraic equations are particularly useful for modeling reallife phenomena.* * *
statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root. Examples are x^{3} + 1 and (y^{4}x^{2} + 2xy – y)/(x – 1) = 12. An important special case of such equations is that of polynomial equations, expressions of the form ax^{n} + bx^{n − 1} + … + gx + h = k. They have as many solutions as their degree (n), and the search for their solutions stimulated much of the development of classical and modern algebra. Equations like x sin (x) = c that involve nonalgebraic operations, such as logarithms or trigonometric functions, are said to be transcendental.The solution of an algebraic equation is the process of finding a number or set of numbers that, if substituted for the variables in the equation, reduce it to an identity. Such a number is called a root of the equation. See also Diophantine equation; linear equation; quadratic equation.* * *
Universalium. 2010.
Look at other dictionaries:
Algebraic equation — In mathematics, an algebraic equation over a given field is an equation of the form:P = Qwhere P and Q are (possibly multivariate) polynomials over that field. For example:y^4+frac{xy}{2}=frac{x^3}{3} xy^2+y^2 frac{1}{7} is an algebraic equation… … Wikipedia
algebraic equation — noun A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3 … Wiktionary
algebraic equation — noun : an equation obtained by equating to zero a sum of a finite number of terms each one of which is a product of positive integral powers (including the zero power) of the variables * * * Math. an equation in the form of a polynomial having a… … Useful english dictionary
Differential algebraic equation — In mathematics, differential algebraic equations (DAEs) are a general form of (systems of) differential equations for vector–valued functions x in one independent variable t, where is a vector of dependent variables and the system has as many… … Wikipedia
Equation — E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night.… … The Collaborative International Dictionary of English
Equation box — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… … The Collaborative International Dictionary of English
Equation clock — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… … The Collaborative International Dictionary of English
Equation of a curve — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… … The Collaborative International Dictionary of English
Equation of equinoxes — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… … The Collaborative International Dictionary of English
Equation of payments — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… … The Collaborative International Dictionary of English