David first discovered this relationship between the roots and coefficients of algebraic equations, so people called this relationship Vieta Theorem. David got this theorem in16th century. The proof of this theorem depends on the basic theorem of algebra, but the basic theorem of algebra was first discussed by Gauss in 1799.
Vieta's theorem plays a unique role in finding the symmetric function of roots, discussing the sign of roots of quadratic equations, solving symmetric equations and solving some conic problems. The discriminant of roots is a necessary and sufficient condition for judging whether an equation has real roots. Vieta theorem explains the relationship between roots and coefficients. Whether the equation has real roots or not, Vieta's theorem is applicable between the roots and coefficients of a quadratic equation with real coefficients. The combination of discriminant and Vieta's theorem can more effectively explain and judge the conditions and characteristics of the roots of a quadratic equation with one variable.
The most important contribution of Vieta's theorem is the promotion of algebra. Firstly, he systematically introduced algebraic symbols, promoted the development of equation theory, replaced unknowns with letters, and pointed out the relationship between roots and coefficients. Vieta's theorem laid a foundation for the study of the unary equation in mathematics, and created and opened up a broad development space for the application of the unary equation.