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Solving 2nd Degree Equations ax2 + bx + c =3D 0
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Solving 2nd Degree Equations ax2 + bx + c =3D 0
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d.= 3;
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d.
II. Then x =3D ±Öd are the roots.
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0079.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d.
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d.
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
3x – 7 =3D 0 solve for x2
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d.
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
3x – 7 =3D 0 solve for x2
3x =3D 7
x2 =3D        = ;        
7
3
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d.
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
3x – 7 =3D 0 solve for x2
3x =3D 7
x2 =3D        = ;         take square root
 =
x =3D ±Ö<= /span>7/3
7
3
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
3x – 7 =3D 0 solve for x2
3x =3D 7
x2 =3D        = ;         take square root
 =
x =3D ±Ö<= /span>7/3 » ±1.53=
7
3
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
3x – 7 =3D 0 solve for x2
3x =3D 7
x2 =3D        = ;         take square root
 =
x =3D ±Ö<= /span>7/3 » ±1.53=
7
3
exact answers 
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
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Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;      The Square-Root Method
Use the square-root method if there is no x-term.
I. Solve for the x and get the form x2 =3D d
II. Then x =3D ±Öd are the roots.
Example A. Solve 3x2 – 7 =3D 0
3x – 7 =3D 0 solve for x2
3x =3D 7
x2 =3D        = ;         take square root
 =
x =3D ±Ö<= /span>7/3 » ±1.53=
7
3
exact answers 
approx. answers
To solve = ax2 + bx + c =3D 0:
1st:  Use the square-root method if the x-term is missing.
2nd: Try factoring it into two binomials.
3rd:  Use the quadratic formula (QF).
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        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Solving 2nd Degree Equations ax2 + bx + c =3D 0
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        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0 
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8) =
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8  
b2 – 4ac =3D (–2)2 – 4(3)(-8)=
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Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8  
b2 – 4ac =3D (–2)2 – 4(3)(-8)   <= /div>
=3D 4 + 96 =3D 100
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0096.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8  
b2 – 4ac =3D (–2)2 – 4(3)(-8)   <= /div>
=3D 4 + 96 =3D 100 =3D 102
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8  
b2 – 4ac =3D (–2)2 – 4(3)(-8)   <= /div>
=3D 4 + 96 =3D 100 =3D 102
So its factorable.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8  
b2 – 4ac =3D (–2)2 – 4(3)(-8)   <= /div>
=3D 4 + 96 =3D 100 =3D 102
So its factorable.
3x= 2 – 2x – 8 =3D 0<= span lang=3DEN-US style=3D'mso-hansi-font-family:Garamond;font-size:75%;color:#= 006600; mso-fareast-language:ZH-CN'>  
(3x + 4)(x – 2) =3D 0
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0099.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Example B.  Which of the following equations is factorable? Solve it = by factoring if it is.
a. 3x2 – 2x + 8 =3D 0        = ;     
   a =3D 3, b =3D= –2, c =3D8        = ;          
   so b = – 4ac        = ;            &n= bsp;        
   =3D (–2)2 – 4(3)(8)<= span style=3D'mso-spacerun:yes'>        = ;           
   =3D 4 <= span lang=3DEN-US style=3D'font-family:Arial;mso-hansi-font-family:Arial;font-s= ize: 75%;color:#006600;mso-fareast-language:ZH-CN'>– 96 =3D –92        = ;            &n= bsp;   
Not a perfect square        = ;      
   so it's not factorable        = ;            &n= bsp;            = ;            &n= bsp;            = ;  
        = ;            &n= bsp;          Factoring Method
Factor the equation into the form (#x + #)(#x + #) =3D 0.
Hint:  Find b2 – 4ac, if it is not a perfec= t square then the= equation = is not factorab= le. (perfect squares: 0, 1, 4, 9, 16,…)
Solving 2nd Degree Equations ax2 + bx + c =3D 0
b. 3x2 – 2x – 8 =3D 0<= /div>
a =3D 3, b =3D –2, c =3D –8  
b2 – 4ac =3D (–2)2 – 4(3)(-8)   <= /div>
=3D 4 + 96 =3D 100 =3D 102
So its factorable.
3x= 2 – 2x – 8 =3D 0<= span lang=3DEN-US style=3D'mso-hansi-font-family:Garamond;font-size:75%;color:#= 006600; mso-fareast-language:ZH-CN'>  
(3x + 4)(x – 2) =3D 0
x =3D -4/3,  x =3D 2
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Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;   Use the quadratic formula (QF)
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0102.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0103.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0<= /div>
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0106.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0
Check if = it is factorable:  a =3D 3,  b =3D –2,  c =3D –2
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0107.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0
Check if = it is factorable:  a =3D 3,  b =3D –2,  c =3D –2
So b2 – 4ac =3D (–2)<= span lang=3DEN-US style=3D'font-size:50%;color:#006600;position:relative;top:-.= 45em; mso-text-raise:30%;mso-fareast-language:ZH-CN'>2 – 4(3)(–2) =3D 28. 
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0108.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0
Check if = it is factorable:  a =3D 3,  b =3D –2,  c =3D –2
So b2 – 4ac =3D (–2)<= span lang=3DEN-US style=3D'font-size:50%;color:#006600;position:relative;top:-.= 45em; mso-text-raise:30%;mso-fareast-language:ZH-CN'>2 – 4(3)(–2) =3D 28.    Not factorable!
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0109.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0
Check if = it is factorable:  a =3D 3,  b =3D –2,  c =3D –2
So b2 – 4ac =3D (–2)<= span lang=3DEN-US style=3D'font-size:50%;color:#006600;position:relative;top:-.= 45em; mso-text-raise:30%;mso-fareast-language:ZH-CN'>2 – 4(3)(–2) =3D 28.    Not factorable! <= /span>
Use QF, we get
x =3D
– (–2) ± Ö 28
2(3)
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0110.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0
Check if = it is factorable:  a =3D 3,  b =3D –2,  c =3D –2
So b2 – 4ac =3D (–2)<= span lang=3DEN-US style=3D'font-size:50%;color:#006600;position:relative;top:-.= 45em; mso-text-raise:30%;mso-fareast-language:ZH-CN'>2 – 4(3)(–2) =3D 28.    Not factorable! <= /span>
Use QF, we get
x =3D
– (–2) ± Ö 28
2(3)
=3D
2 ± Ö 28
6
        = ;            &n= bsp;   Use the quadratic formula (QF)
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            &n= bsp;
x =3D = 3;
 
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >discriminant because = its value indicates what type of roots there are. Specifically,
if b2 – 4ac is a perfect square, w= e have fractional roots,
if b2 – 4ac < 0 there is no real roots.
------=_NextPart_01C9D949.BBEC5F00 Content-Location: file:///C:/09764A33/3Solving2ndDegreeEquations_files/slide0111.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
–b±Ö b= 2 – 4ac
2a
Solving 2nd Degree Equations ax2 + bx + c =3D 0
Example C= .  Solve 3x2 – 2x – 2 =3D 0
Check if = it is factorable:  a =3D 3,  b =3D –2,  c =3D –2
So b2 – 4ac =3D (–2)<= span lang=3DEN-US style=3D'font-size:50%;color:#006600;position:relative;top:-.= 45em; mso-text-raise:30%;mso-fareast-language:ZH-CN'>2 – 4(3)(–2) =3D 28.    Not factorable! <= /span>
Use QF, we get
x =3D
– (–2) ± Ö 28
2(3)
=3D
2 ± Ö 28
6
=3D
2 ± 2<= /span>Ö7