History Of Polynomial Equations
Quadratic - Page Three



ViËte was among the first to replace geometric methods of solution with analytic ones, although
he apparently did not grasp the idea of a general
quadratic equation


Part Two: Solving The Quadratic (Theory)

A quadratic equation is a second-order polynomial equation in a single variable x
ax^2 + bx + c = 0
(with a≠0).

Because it is a second-order polynomial equation,
the fundamental theorem of algebra guarantees
that it has two solutions. These solutions may be
both real, or both complex.

1 - History
2 - Quadratics
3 - Cubic
4 - Quartic
5 - Quintic
6 - Appendix



The roots x can be found by completing the square,
x^2 + (b/a)x = -(c/a)

(x + b/(2a))^2 = - (c/a) + b^2 / (4a^2) = (b^2 - 4ac)/(4a^2)

x + b/(2a) = (+/-sqrt(b^2 - 4ac)) / (2a)

Solving for x then gives:

x = (-b +/-sqrt(b^2 - 4ac)) / (2a)

This equation is known as the quadratic formula.
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by thomas m. bösel @ www.vimagic.de for University Of Adelaide - History Of Mathematics 2002