In algebra, a quadratic equation (from Latin quadratus 'square') is any 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...

zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros of the corresponding quadratic function. The bivariate...

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is ax2+bx+c=0,{\displaystyle ax^{2}+bx+c=0,} where...

inside of a quadratic expression. Completing the square is used in solving quadratic equations, deriving the quadratic formula, graphing quadratic functions...

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}...

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 +...

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

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

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...

circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given...

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...

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...

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...

not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadratic form is one case of the...

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...

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

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...

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...

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

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

closed form algebraic equation that isolates the variable on one side. For example, the general solution to quadratic equations of the form a x 2 + b...

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

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

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

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...

conic Dome § Paraboloid dome Parabolic partial differential equation Quadratic equation Quadratic function Universal parabolic constant Confocal conic sections...

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...

For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables...

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