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An algebraic equation of the second degree. The general form of a quadratic equation is In the field of complex numbers a quadratic equation has two solutions, expressed by radicals in the coefficients of the equation: (*)

When both solutions are real and distinct, when , they are complex (complex-conjugate) numbers, when the equation has the double root .

For the reduced quadratic equation formula (*) has the form The roots and coefficients of a quadratic equation are related by (cf. Viète theorem): The expression is called the discriminant of the equation. It is easily proved that , in accordance with the fact mentioned above that the equation has a double root if and only if . See also Discriminant. Formula (*) holds also if the coefficients belong to a field with characteristic different from 2.
Formula (*) follows from writing the left-hand side of the equation as (splitting of the square).