Formulas of Viète

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With the formulae of Viète, the coefficients of a quadratic function can be expressed in the sum and the product of its zeros, by

and

The general form of a quadratuc function is

what you can also write as

because it applies that a ≠ 0, otherwise it would not be a second-grade function. If you factorize this function you get

A calculation then gives

so that

and

The formulas were developed by the French mathematician François Viète.