algebraic equation
an equation in the form of a polynomial having a finite number of terms and equated to zero, as 2x3 + 4x2 - x + 7 = 0.

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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 = ax2 + 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 real-life phenomena.

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      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 x3 + 1 and (y4x2 + 2xy – y)/(x – 1) = 12. An important special case of such equations is that of polynomial equations, expressions of the form axn + bxn − 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.

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Universalium. 2010.

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