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 {\displaystyle b^{2}-4ac>0}, then the quadratic equation has two distinct real solutions; if {\displaystyle b^{2}-4ac=0}, the equation has two real solutions which are equal; if {\displaystyle 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.\,
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