### ::concepts

Equation::''x''    Roots::formula    First::square    ''c''::''a''    Title::function    ''b''::books

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For the case of more than one variable, see Conic section or Quadratic form.

In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form

[itex]ax^2+bx+c=0[/itex]

where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.<ref>Protters & Morrey: " Calculus and Analytic Geometry. First Course"</ref>

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.

Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using the quadratic formula, or by graphing. Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC.