Quadratic equation

In mathematics, a quadratic equation is a polynomial equation of the second degree. The generalized form is

Generalizations

The formula and its proof remain correct if the coefficients a, b and c are complex numbers, or more generally members of any field whose characteristic is not 2. (In a field of characteristic 2, the element 2a is zero and it is impossible to divide by it.)

Related Topics:
Complex number - Field - Characteristic

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The symbol

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:pm sqrt {b^2-4ac }

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in the formula should be understood as "either of the two elements whose square is b2 − 4ac, if such elements exist". In some fields, some elements have no square roots and some have two; only zero has just one square root, except in fields of characteristic 2.

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