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{{Portal:Mathematics/Feature article|img=Polynomialdeg2.png|img-cap=The graph of a [[real number|real-valued]] quadratic function of a real variable ''x'', is a [[parabola]].|img-cred=[[User:Enochlau|Enoch Lau]]|more=Quadratic equation|desc=A '''quadratic equation''' is a [[polynomial]] [[equation]] of [[degree of a polynomial|degree]] two. The general form is | |||
:<math>ax^2+bx+c=0,\,\!</math> | |||
where ''a'' ≠ 0 (if ''a'' = 0, then the equation becomes a [[linear equation]]). The letters ''a'', ''b'', and ''c'' are called [[coefficient]]s: the quadratic coefficient ''a'' is the coefficient of ''x''<sup>2</sup>, the linear coefficient ''b'' is the coefficient of ''x'', and ''c'' is the [[constant]] coefficient, also called the ''free term''. | |||
Quadratic equations are called ''quadratic'' because ''quadratus'' is [[Latin]] for "square"; in the leading term the variable is [[square (algebra)|squared]]. | |||
A quadratic equation has two (not necessarily distinct) solutions, which may be [[real number|real]] or [[complex number|complex]], given by the '''quadratic formula''': | |||
:<math>x = \frac{-b \pm \sqrt {b^2-4ac}}{2a},</math> | |||
These solutions are [[root (mathematics)|''roots'']] of the corresponding [[quadratic function]] | |||
:<math>f(x) = ax^2+bx+c.\,</math>|class={{{class}}}}} | |||
<noinclude>{{../Footer}}</noinclude> | |||
Revision as of 10:15, 29 December 2013
{{../Header}} Template:Portal:Mathematics/Feature article {{../Footer}}