Vieta's theorem explains the relationship between roots and coefficients in a quadratic equation with one variable. French mathematician Francois Viete established the relationship between roots and coefficients in the identification and correction of equations in his works of 16 15, and put forward this theorem. Because David first discovered this relationship between the roots and coefficients of algebraic equations, people call this relationship the Vieta theorem.
The content of Vieta's theorem
The discriminant of the root of a quadratic equation is a, b and c, which are quadratic coefficient, linear coefficient and constant term of the quadratic equation. The relationship between Vieta's theorem and the discriminant of roots is even more inseparable. 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, the relationship between roots and coefficients of a quadratic equation with real coefficients is applicable to Vieta's theorem. 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 to promote 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 developed a broad development space for the application of the unary equation. Vieta theorem can be used to quickly find the relationship between the roots of two equations. Vieta theorem is widely used, which is reflected in elementary mathematics, analytic geometry, plane geometry and equation theory.