Portal:Mathematics/Selected article/31

{{Portal:Mathematics/Feature article|img=Polynomialdeg2.png|img-cap=The graph of a real-valued quadratic function of a real variable x, is a parabola.|img-cred=Enoch Lau|more=Quadratic equation|desc=A quadratic equation is a polynomial equation of degree two. The general form is

: $ax^2+bx+c=0,\,\!$

where a ≠ 0 (if a = 0, then the equation becomes a linear equation). The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x², the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term.

Quadratic equations are known by that name because quadratus is Latin for "square"; in the leading term the variable is squared.

A quadratic equation has two (not necessarily distinct) solutions, which may be real or complex, given by the quadratic formula:

: $x = \frac{-b \pm \sqrt {b^2-4ac}}{2a},$

If the discriminant $b^2-4ac>0$ , then the quadratic equation has two distinct real solutions; if $b^2-4ac=0$ , the equation has two real solutions which are equal; if $b^2-4ac<0$ , the equation has two complex solutions.

These solutions are roots of the corresponding quadratic function

: $f(x) = ax^2+bx+c.\,$ |class={{{class}}}}}