In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle...

the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such...

parabola. If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros (or...

degree 2; that is, as the set of points whose coordinates satisfy a quadratic equation in two variables which can be written in the form A x 2 + B x y +...

quadratic equation with rational coefficients which is irreducible over the rational numbers. Since fractions in the coefficients of a quadratic equation can...

dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main...

a_{0}z^{2}+a_{2}z+a_{4}=0\,\!} which is a simple quadratic equation, whose solutions are easily found using the quadratic formula: z = − a 2 ± a 2 2 − 4 a 0 a 4...

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0...

numbers first arise in the teaching of quadratic equations and the quadratic formula. For example, the quadratic equation x 2 + x + 1 = 0 {\displaystyle x^{2}+x+1=0}...

BC could solve some kinds of quadratic equations (displayed on Old Babylonian clay tablets). Univariate algebraic equations over the rationals (i.e., with...

The treatise provided for the systematic solution of linear and quadratic equations. According to one history, "[i]t is not certain just what the terms...

the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime...

following examples. Consider the quadratic equation x 2 − 4 x + 1 = 0. {\displaystyle x^{2}-4x+1=0.} By using the quadratic formula, we find that the two...

to an equation using Vieta's formulas. Vieta jumping is a classical method in the theory of quadratic Diophantine equations and binary quadratic forms...

⁠. Completing the square is the oldest method of solving general quadratic equations, used in Old Babylonian clay tablets dating from 1800–1600 BCE, and...

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...

to be confused with quadratic equations, which have only one variable and may include terms of degree less than two. A quadratic form is a specific instance...

the case of linear and quadratic equations, was an achievement of the twentieth century. In the following Diophantine equations, w, x, y, and z are the...

the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square. Quadratic function (or quadratic polynomial), a polynomial...

tangent line at that point, or as the solution of certain bivariate quadratic equations such as the reciprocal relationship x y = 1. {\displaystyle xy=1...

This is typically the case when considering polynomial equations, such as quadratic equations. However, for some problems, all variables may assume either...

In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function....

operations with equations described in this book, following its Latin translation by Robert of Chester. The book classifies quadratic equations to one of the...

the quadratic equation a0z2 + a1z + a2 − 2ma0 = 0. Since x2 − xz + m = 0, the quartic equation P(x) = 0 may be solved by applying the quadratic formula...

acids, a quadratic equation must be solved, and for weak bases, a cubic equation is required. In general, a set of non-linear simultaneous equations must...

14th century both found general solutions to Pell's equation and other quadratic indeterminate equations. Bhaskara II is generally credited with developing...

roots. (This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem...

linear equation for degree one quadratic equation for degree two cubic equation for degree three quartic equation for degree four quintic equation for degree...

C 1, D 3.) Quadratic equations of the form a x 2 + b x + c = 0 {\displaystyle ax^{2}+bx+c=0} can be solved by first reducing the equation to the form...

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field...