二次方程 (1) ( 解方程 - 因式法 ) Name:______________Class:_____( )Date:__________

學習目標：(1) 用因式法解二次方程。重點：(1) 因式法： A若 ×B=0，則 A=0 B或 =0

(2) 應用因式法解二次方程：若( Ax+B)(Cx+D)=0，則Ax+B=0或Cx+D=0

1. 解二次方程 (x + 4)(2x– 1) = 0。 2. 解二次方程 4x(3x + 2) = 0。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. 解二次方程x2−14 x+45=0。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

4. 解二次方程x2−8 x=0。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. 解二次方程9 x+2x2−18=0。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. 解二次方程x2+ 3 x

2=7 。

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Intro: HW:

7. 解二次方程4 x2−25=0 。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________8. 解二次方程 (x– 1)(x + 2) = 10。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________9. 解二次方程 (3x + 1)(x– 4) –x = 11。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

10. 解二次方程( x−3 )2+6=2x。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

11. 解二次方程( x−1)2=(2x+3 )2。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

12. 假設–2 是二次方程2 x2−x+( k+1)=0的根。(a) 求 k的值。(b) 求方程的另一個根。

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13. 假設–3 是二次方程x2+2 x−11−k ( x−1 )=0 的根。(a) 求 k的值。(b) 求方程的另一個根。

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Quadratic Equation (1) (Solve Equation – Factor Method) Name:______________Class:_____( )Date:_________

Objective:(1) Solving quadratic equation by using factor method.Main Point:(1) Factor Method: IfA×B=0 , thenA=0or B=0(2) Solving quadratic equation by using factor method.

If( Ax+B)(Cx+D)=0 , thenAx+B=0orCx+D=0

1. Solve equation (x + 4)(2x– 1) = 0。 2. Solve equation 4x(3x + 2) = 0。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. Solve equation x2−14 x+45=0。

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4. Solve equation x2−8 x=0 。

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5. Solve equation 9 x+2x2−18=0。______________________________________________________________________________________________________________________________________________________________________________

Intro: HW:

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6. Solve equation x2+ 3 x

2=7 。

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7. Solve equation 4 x2−25=0 。

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________8. Solve equation (x– 1)(x + 2) = 10。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________9. Solve equation (3x + 1)(x– 4) –x = 11。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

10. Solve equation ( x−3 )2+6=2x。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

11. Solve equation ( x−1)2=(2x+3 )2。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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12. Let –2 be the root of the equation2 x2−x+( k+1)=0 .

(a) Find the value of k.(b) Find another root of the equation.

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13. Let –3 be the root of the equationx2+2 x−11−k ( x−1 )=0 .

(a) Find the value of k.(b) Find another root of the equation.

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二次方程 (解方程 - 因式法)

Name:_______________________ Class:_____________( ) Date:_________________

若( Ax+B)(Cx+D) .. .(Ex+F )=0 ,

則Ax+B=0，或Cx+D=0，或 Ex+F=0

1. ( x+4 )(2 x−1)=0

x+4=0 或2 x−1=0

x=−4 或 x= 12

2. 4 x(3 x+2)=0

4 x=0 或3 x+2=0

x=0 或 x=−23

3. x2−14 x+45=0( x−5 )(x−9 )=0

x= 5 或 9

4 x2−8 x=0x ( x−8 )=0

x= 0 或 8 5. 9 x+2x2−18=0

2 x2+9 x−18=0

(2x−3)( x+6 )=0

x=−6 或 32

6.x2+ 3 x

2=7

2 x2+3 x−14=0

( x−2 )(2 x+7 )=0

x=−72

或 2

7. 4 x2−25=0

(2x )2−52=0(2x−5)(2 x+5)=0

x=−52

或 52

8. ( x−1)( x+2 )=10

x2+x−2=10

x2+x−12=0

( x−3 )( x+4 )=0

x= 4 或 3

9.(3 x+1 )( x−4 )−x=113x2−11 x−4−x=11

3 x2−12 x−15=0

x2−4 x−5=0

( x+1)( x−5 )=0

x= 1 或 5

10.( x−3 )2+6=2x( x−3 )2+6−2x=0

( x−3 )2+2(3−x )=0

( x−3 )2−2 (x−3)=0( x−3 )( x−3−2 )=0( x−3 )( x−5)=0

x= 3 或 5 11. ( x−1)2=(2x+3 )2

( x−1)2−(2x+3 )2=0[( x−1)−(2 x+3 ) ][( x−1)+(2x+3 )]=0( x−1−2 x−3 )( x−1+2 x+3 )=0

(−x−4 )(3 x+2)=0

( x+4 )(3 x+2)=0

x=−4 或 −23

12 (a) ∵ −2為方程的根。∴ 2(−2)2−(−2 )+(k+1 )=0

10+k+1=0

k+11=0

k=−11(b) 方程為

2 x2−x−10=0

(2x−5)( x+2)=0

x=−2 或 52 ∴ 另一個根為

52 。

13. (a) ∵ −3為方程的根。∴ (−3)2+2(−3 )−11−k (−3−1)=0

9−6−11+4 k=0

4 k−8=0

k=2(b) 方程為

x2+2 x−11−2( x−1)=0x2+2 x−11−2x+2=0

x2−9=0

x2=9

x=±3 ∴ 另一個根為 3。