< 1 2 >
Formulas of Viète
With the formulas of Viète, the coefficients of a quadratic function can be expressed in the sum and the product of its zeros, by
and
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
Additional information
The formulas were developed by the French mathematician François Viète.