In the middle, two x's? 、x？ Have the following relationship:

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.

Extended data

Vieta's theorem is mainly used to solve the problems related to two roots of a quadratic equation with one variable. The appearance of this theorem saves time for solving similar problems.

Vieta's theorem (), simply put, can be directly obtained by the correlation coefficient of a quadratic equation. In the above formula, a is the coefficient before the second power, b is the coefficient before the first power, and c is a constant term, which is a relatively direct and practical method.

Especially for those problems with two known roots that need to derive equations, the advantages of Vieta's theorem can be better reflected. Vieta theorem can also be used in higher-order equations, and the summation formula will be involved in the solution process.

Baidu encyclopedia-Vieta theorem