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Formulas of Viète

Using Viète's formulas, the sum and product of the zeros of a quadratic function can be expressed by its coefficients, as

     and     

 

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Explanation

The general form of a quadratic 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     

 

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History The formulas were developed by the French mathematician François Viète (1540 - 1603).

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