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"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.
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