"Solving Quadratic Equations of One Variable by Factoring Method" Quadratic Equations of One Variable PPT Courseware 3

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"Solving Quadratic Equations of One Variable by Factoring Method" Quadratic Equations of One Variable PPT Courseware 3

Steps to solve quadratic equations of one variable using the formula method:

1. Transform to 1: Change the coefficient of the quadratic term to 1 (divide both sides of the equation by the coefficient of the quadratic term);

2. Move the term: Move the constant term to the right side of the equation;

3. Recipe: Add half the square of the absolute value of the coefficient of the linear term to both sides of the equation;

4. Deformation: factorize the left side of the equation and combine similar factors on the right side;

5. Square root: According to the meaning of square root, the square root of both sides of the equation;

6. Solve: Solve linear equations of one variable;

7. Definite solution: Write the solution of the original equation.

When one side of a quadratic equation is 0 and the other side is easily decomposed into the product of two linear factors, we can solve it by factoring. This method of solving a quadratic equation by factoring you is the factoring method.

Teacher Tips:

1. The conditions for using the decomposition factor method are: the left side of the equation is easy to decompose, and the right side is equal to zero;

2. The key is to master the knowledge of factorization;

3. The theory is still "If the product of two factors is equal to zero, then at least one factor is equal to zero."

Generally speaking, to decompose the quadratic trinomial ax²+bx+c(a≠o) within the range of real numbers, you only need to use the formula method to find the corresponding quadratic equation ax²+bx+c=0(a≠o), The two roots x1, x2, and then directly write ax²+bx+c as a(x-x1)(x-x2), that’s it.

That is, ax²+bx+c= a(x-x1)(x-x2).

The steps to solve a quadratic equation of one variable by factoring are:

1. Transform the equation into a general form;

2. Factor the left side of the equation;

3. According to "at least one factor is zero", convert it into two linear equations of one variable.

4. Solve two linear equations of one variable respectively, and their roots are the roots of the original equation.

The combination method and the formula method are important methods for solving quadratic equations of one variable and should be mastered as a basic skill. Some equations can be solved easily and quickly using the factorization method.

The quadratic equation is also an effective mathematical model to describe the real world.

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For more information about the PPT courseware "Using Factorization Method to Solve Quadratic Equations of One Dimension and Quadratic Equations of One Dimension", please click the Solving Quadratic Equations of One Dimension Using Factorization Method ppt Quadratic Equations ppt tag.

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Update Time: 2024-10-21

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