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quadratic equation

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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.

© Research Machines plc 2008. All rights reserved. Helicon Publishing is a division of Research Machines plc.


 
 

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