"Solving quadratic equations of one variable using factoring method" PPT courseware 3

Description

"Solving quadratic equations of one variable using factoring method" PPT courseware 3

Review and review

We obtain the roots of quadratic equations by completing the square method. This method of solving quadratic equations is called solving by completing the square.

Assistant for solving quadratic equations of one variable using the combination method:

The meaning of square root: If x2=a, then x=±√a

Perfectly square method: The formula a2±2ab+b2 is called a perfectly square method, and a2±2ab+b2 = (a±b)2.

factoring method

When one side of a quadratic equation is 0 and the other side is easy to decompose 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."

Appreciation of examples

Example 1. Solve the equation:

(1)15x2+6x=0; (2) 4x2-9=0.

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.

Can you solve the following equation using factoring?

1.x2-4=0; 2.(x+1)2-25=0.

Solution: 1.(x+2)(x-2)=0, 2.[(x+1)+5][(x+1)-5]=0,

∴x+2=0, or x-2=0. ∴x+6=0, or x-4=0.

∴x1=-2, x2=2. ∴x1=-6, x2=4.

Is this solution the best way to solve these two equations?

Do you have any other ways to solve it?

Summary and expansion

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 is called is the factoring method.

The condition of the factorization method is that the left side of the equation is easy to factor, and the right side is equal to zero. The key is to master the knowledge of factorization. The theory is still "if the product of two factors is equal to zero, then at least one factor is equal to zero."

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", two linear equations of one variable are obtained.

(4) The roots of two linear equations of one variable are the roots of the original equation.

The method of factorization highlights the thinking method of transformation - "reduction", and clearly shows the process of transforming "secondary" into "primary".

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

"Solving quadratic equations of one variable using factoring method" PPT courseware 2:

"Using Factorization Method to Solve Quadratic Equations" PPT Courseware 2 Review Introduction: 1. What are the methods for solving quadratic equations that have been learned? 2. Please use the method you have learned to solve the equation x-4=0 x2-4=0 Solution: The original equation can be transformed into (x+2)(x-2)=0 AB=0 A=0 or B..

"Solving quadratic equations of one variable using factoring method" PPT courseware:

"Using Factorization Method to Solve Quadratic Equations" PPT courseware Review introduction: 1. What are the methods for solving quadratic equations that have been learned? 2. Please use the method you have learned to solve the equation x-4=0. Steps to solve the quadratic equation by factoring. 1. Change the right side of the equation to ______..

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

"Using Factorization Method to Solve Quadratic Equations" Quadratic Equations PPT Courseware 3 Steps to solve quadratic equations using the factoring method: 1. Transform 1: Change the coefficient of the quadratic term to 1 (divide both sides of the equation by two Coefficient of secondary term); 2.Transfer term: Move the constant term to the right side of the equation; 3.Recipe:..

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Update Time: 2024-10-19

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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