Concept
Quadratic equation
Related concepts (29)
Nested radical
In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include which arises in discussing the regular pentagon, and more complicated ones such as Some nested radicals can be rewritten in a form that is not nested. For example, Another simple example, Rewriting a nested radical in this way is called denesting. This is not always possible, and, even when possible, it is often difficult.
Carlyle circle
In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the property that the solutions of the quadratic equation are the horizontal coordinates of the intersections of the circle with the horizontal axis. Carlyle circles have been used to develop ruler-and-compass constructions of regular polygons.
Solution in radicals
A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of nth roots (square roots, cube roots, and other integer roots). A well-known example is the solution of the quadratic equation There exist more complicated algebraic solutions for cubic equations and quartic equations.
Arithmetica
Arithmetica (Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus (200/214 AD-284/298 AD) in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations.
Brāhmasphuṭasiddhānta
The Brāhma-sphuṭa-siddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is a main work of Brahmagupta, written c. 628. This text of mathematical astronomy contains significant mathematical content, including the first good understanding of the role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and Brahmagupta theorem.
Univariate
In mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one variable are multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials.
Quadratic irrational number
In mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their least common denominator, a quadratic irrational is an irrational root of some quadratic equation with integer coefficients.
Plimpton 322
Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has number 322 in the G.A. Plimpton Collection at Columbia University. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period. This table lists two of the three numbers in what are now called Pythagorean triples, i.e., integers a, b, and c satisfying a2 + b2 = c2.
Sridhara
Śrīdhara, Śrīdharācāryya or Śrīdhara Acharya ( 870 CE – 930 CE) was an Indian mathematician, Sanskrit pandit and philosopher. He was born in Bhuriśreṣṭi (Bhurisriṣṭi or Bhurśuṭ) village in South Rādha at present day Hugli in West Bengal, then undivided Bengal with its Capital at Gaur. His father's name was Baladevācārya or Baladeva Acharya and his mother's name was Acchoka Devi. His father was a Sanskrit pandit . He is known for two main treatises: Trisatika (300) (sometimes called the Patiganitasara ) and the Pāṭīgaṇita (পাটীগণিত).