"Factorization Method for Solving Quadratic Equations of One Variable" PPT courseware

Description

"Factorization Method for Solving Quadratic Equations of One Variable" PPT courseware

General steps for solving quadratic equations of one variable using factorization:

(1) Set the right side of the equation to zero;

(2) Decompose the left side of the equation into _________ of two linear factors;

(3) Let each factor be zero to obtain two linear equations of one variable;

(4) Solve these two linear equations of one variable, and their solutions are the _________ of the original equations.

1. (4 points) (2013·Shaanxi) The root of the quadratic equation x2-3x=0 is ________.

2. (4 points) The solution to the equation x(x-2)+x-2=0 is ()

A． x=2B． x1=-2, x2=1

C. x=-1 D. x1=2, x2=-1

3. (4 points) (2013·Henan) The solution of equation (x-2)(x+3)=0 is ()

A． x=2 B. x=-3

C. x1=-2, x2=3 D． x1=2, x2=-3

4. (4 points) After calculation, the product of the integers x+1 and x-4 is x2-3x-4. Then all the roots of the quadratic equation x2-3x-4=0 are ()

A． x1=-1, x2=-4 B． x1＝-1, x2＝4

C. x1=1, x2=4 D. x1=1, x2=-4

5. (5 points) Use the factoring method to decompose the equation (x-5)(x+1)=7 into two linear equations. The correct one is ()

A． x-5=1, x+1=7 B. x－5＝7，x＋1＝1

C. x+6=0, x-2=0 D． x－6＝0，x＋2＝0

6. (5 points) The following equation cannot be solved by factoring ()

A． x2=3x B． (x-2)2＝3x-6

C. 9x2+6x+1＝0 D. (x+2)(3x-1)＝5

17． (12 points) We know the following n (n is a positive integer) quadratic equations of one variable about x:

x2－1＝0①

x2+x－2＝0②

x2+2x-3＝0③

…

x2+(n-1)x-n＝0○n

(1) Please solve the above quadratic equations ①, ②, ③, ○n;

(2) Please point out what common characteristics the roots of these n equations have. Just write one.

(1)① x1＝-1, x2＝1; ② x1＝-2, x2＝1; ③ x1＝-3, x2＝1; ○n x1＝-n, x2＝1

(2) For example: both have a root of 1; both have a negative integer; both roots are integer roots.

Keywords: teaching courseware on the factorization method of solving quadratic equations of one variable, download the mathematics PPT courseware for the first volume of the ninth grade of the Hebei Education Edition, download the mathematics slide courseware of the ninth grade, download the PPT courseware on the factorization method of solving the quadratic equation of one variable, .PPT format ;

For more information about the PPT courseware "Factorization Method for Solving Quadratic Equations", please click the Factorization Method for Solving Quadratic Equations ppt tag.

File Info

Update Time: 2024-11-21

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

Preview