1. Grasp the relationship between roots and coefficients of a quadratic equation in one variable, and use it to find another root and unknown coefficients from a known root of a quadratic equation in one variable;

2. Through the teaching of roots and coefficients, further cultivate students' ability of analysis, observation, induction and reasoning;

3. Through the teaching of this lesson, let students penetrate the law of things from special to general, and then from general to special.

Teaching emphases and difficulties:

Two. Key points, difficulties, doubts and solutions

1. Teaching emphasis: the relationship between root and coefficient and its derivation.

2. Teaching difficulties: correctly understand the relationship between roots and coefficients.

3. Teaching doubts: The relationship between roots and coefficients of a quadratic equation in one variable refers to the relationship between the sum of two roots of a quadratic equation in one variable and the relationship between the product of two roots and coefficients.

4. Solutions; When applying Vieta's theorem in the real number range, we must pay attention to this premise, and the premise of applying discriminant is that the equation must be a quadratic equation, that is, the quadratic term coefficient. Therefore, when solving problems, it is necessary to analyze whether there are implicit conditions and.

Third, the teaching steps

(A) the teaching process

1. Review the questions

(1) Write the general formula and root of quadratic equation with one variable.

(2) Solve equations ① and ②.

Observe and think about the relationship between two sums, two products and coefficients.

Under the guidance and guidance of the teacher, the teacher draws a conclusion from the heaviness. The teacher asked: Do both roots of a quadratic equation have such a law?

2. Derive the relationship between two sums of a quadratic equation and two product sum coefficients.

Let an equation have two roots.

∴

∴

More than one student writes on the blackboard, and the other students perform in the exercise books.

From this, the relationship between the roots and coefficients of a quadratic equation with one variable is obtained. (The relationship between two sums of quadratic equation with one variable and two product sum coefficients)

Conclusion 1. If the two roots of are, then.

If the equation is deformed into.

We can write it as

In the form of, among them. Therefore, the conclusion is:

Conclusion 2. If the two roots of the equation are, then.

Conclusion 1 has a general form, and conclusion 2 sometimes brings convenience to research problems.

Exercise 1. (Oral answer) What is the sum of two and the product of two in the following equation?

( 1); (2); (3);

(4); (5); (6)

The purpose of this group of exercises is to master the relationship between roots and coefficients more skillfully.