The concrete expression of Vieta's theorem;

In the unary quadratic equation aX 2+bx+c = 0 (a ≠ 0 and △ = b 2-4ac ≥ 0), if the two roots are X 1 and x 2. (△ = b 2-4ac is the discriminant, and△ = b 2-4ac ≥ 0, indicating that the equation has two real numbers).

Then X 1+X2= -b/a, x1* x2 = c/a.

Extended data:

16 15 years, French mathematician Francois Viete improved the solutions of cubic and quartic equations in his book "On the Identification and Correction of Equations", and also established the relationship between the roots and coefficients of equations when n=2 and 3, which is the modern Vieta theorem.

The meaning of Vieta's theorem:

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.

Application of Vieta Theorem:

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.

References:

Baidu encyclopedia-Vieta theorem