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For the case of more than one variable, see Conic section or Quadratic form.
The quadratic formula for the roots of the general quadratic equation

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

<math>ax^2+bx+c=0</math>

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.


Quadratic equation sections
Intro  Examples and applications  Solving the quadratic equation  History  Advanced topics  See also  References  External links  

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{{#invoke:Hatnote|hatnote}}

For the case of more than one variable, see Conic section or Quadratic form.
The quadratic formula for the roots of the general quadratic equation

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

<math>ax^2+bx+c=0</math>

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.


Quadratic equation sections
Intro  Examples and applications  Solving the quadratic equation  History  Advanced topics  See also  References  External links  

PREVIOUS: IntroNEXT: Examples and applications
<<>>