Let a binary linear equation be: ax 2+bx+c = 0, where a is not 0, because a cannot be equal to 0 to satisfy this equation. The root formula is: x1= (-b+(B2-4ac)1/2)/2a, x2 =

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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 the root of a quadratic equation with one variable is (A, B and C are quadratic coefficient, linear coefficient and constant term of the quadratic equation with one variable respectively). 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, 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.

Vieta theorem can be used to quickly find out the relationship between the roots of two equations. Vieta theorem is widely used in elementary mathematics, analytic geometry, plane geometry and equation theory.

Baidu encyclopedia-Vieta theorem