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
A quadratic equation is a second-order polynomial equation in a single variable x
(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.
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The roots x can be found by completing the square,
Solving for x then gives:
This equation is known as the quadratic formula.
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