## ::Quadratic equation

### ::concepts

{{#invoke:Hatnote|hatnote}}

*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

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

{{#invoke:Hatnote|hatnote}}

*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

- <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: Intro | NEXT: Examples and applications |

<< | >> |