quadratic equation

In mathematics, a polynomial equation of second degree (that is, an equation containing as its highest power the square of a variable, such as x²). The general formula of such equations is

ax² + bx + c = 0

in which a, b, and c are real numbers, and only the coefficient a cannot equal 0.

In coordinate geometry, a quadratic function represents a parabola.

Some quadratic equations can be solved by factorization (see factor (algebra)), or the values of x can be found by using the formula for the general solution

x = [-b + √(b² - 4ac)]/2a or

x = [-b - √(b² - 4ac)]/2a

Depending on the value of the discriminant, b² - 4ac, a quadratic equation has two real, two equal, or two complex roots (solutions). When b² - 4ac > 0, there are two distinct real roots. When b² - 4ac = 0, there are two equal real roots. When b² - 4ac < 0, there are two distinct complex roots.