ARTICLE
from the
Encyclopædia Britannica
algebraic equation, 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.
Aspects of the topic algebraic equation are discussed in the following places at Britannica.
Assorted References
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major reference (in elementary algebra: Solving algebraic equations)
For theoretical work and applications one often needs to find numbers that, when substituted for the unknown, make a certain polynomial equal to zero. Such a number is called a “root” of the polynomial. For example, the polynomial −16t2 + 88t + 48represents the height above Earth at t seconds of a...
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history of mathematics (in mathematics: Analytic geometry)
Following the important results achieved in the 16th century by Gerolamo Cardano and the Italian algebraists, the theory of algebraic equations reached an impasse. The ideas needed to investigate equations of degree higher than four were slow to develop. The immediate historical influence of Viète, Fermat, and Descartes was to furnish algebraic methods for the investigation of curves. A...
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solution by Gauss (in Carl Friedrich Gauss (German mathematician))
...a regular polygon of 17 sides can be constructed by ruler and compass alone. Its significance lies not in the result but in the proof, which rested on a profound analysis of the factorization of polynomial equations and opened the door to later ideas of Galois theory. His doctoral thesis of 1797 gave a proof of the fundamental theorem of algebra: every polynomial equation with real or...
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use in analytic geometry (in analytic geometry)
...which algebraic symbolism and methods are used to represent and solve problems in geometry. The importance of analytic geometry is that it establishes a correspondence between geometric curves and algebraic equations. This correspondence makes it possible to reformulate problems in geometry as equivalent problems in algebra, and vice versa; the methods of either subject can then be used to...
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work of Viète (in algebra (mathematics): Viète and the formal equation)
It is in the work of the French mathematician François Viète that the first consistent, coherent, and systematic conception of an algebraic equation in the modern sense appeared. A main innovation of Viète’s In artem analyticam isagoge (1591; “Introduction to the Analytic Art”) was its use of well-chosen symbols of one kind (vowels) for unknowns and...
People
The following are some people associated with "algebraic equation"
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The following is a selection of items (artistic styles or groups, constructions, events, fictional characters, organizations, publications) associated with "algebraic equation"
The topic algebraic equation is discussed at the following external Web sites.
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Wolfram MathWorld - Algebraic Equation
