CN4B_quadratics_review

## Quadratics Review

Solve for x:

x^2 - 11x - 26 = 0
(x - 13)(x + 2) = 0

x^2 + 8x - 20 = 0
(x - 2)(x + 10) = 0

x^2 + 4x - 21 = 0
(x + 7)(x - 3) = 0

x^2 + x - 2 = 0
(x + 2)(x - 1) = 0

x^2 + 13x + 40 = 0
(x + 8)(x + 5) = 0

x^2 + 2x - 99 = 0
(x - 9)(x + 11) = 0

x^2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)^2 = 0

x^2 - 14x + 24 = 0
(x - 12)(x - 2) = 0
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Solve for x:
                              ax^2 + bx + c = 0
                              
                              -b +/- sqrt(b^2 - 4ac)
                              ----------------------
                                      2a
3x^2 + 15x + 18 = 0
(3x + 9)(x + 2) = 0

6x^2 - 5x - 4 = 0

   5 +/- sqrt(121)
------------------------
          12
   
   5 +/- 11
   --------
      12
     
     roots = 1.333 , -0.5
        
        

16x^2 + 0x - 49 = 0
(4x + 7)(4x - 7) = 0

12x^2 + 17x - 5 = 0

       -17 +/- 23
----------------------------
           24
roots = 0.25 and -40/24
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Solve for x:

24x^2 - 18x + 0 = 0
4x^2 - 3x = 0
x(4x - 3) = 0 

2 - 8x^2 = 0
8x^2 + 0x - 2 = 0
4x^2 - 1 = 0
(2x + 1)(2x - 1) = 0


3x^2 - 27 = 0
(x + 3)(x - 3) = 0

x^2 - 6x + 2 = 0

sqrt(a)/sqrt(b) = sqrt(a/b)

   6 +/- sqrt(28)
---------------------
        sqrt(4)
        
  3 +/- sqrt(7)

roots = (3 + sqrt(7)), (3 - sqrt(7))
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Solve:

52k + 12 = 9k^2
0 = 9k^2 - 52k - 12
0 = (9k + 2)(k - 6)
k = 6
k = -2/9


3h^2 - 4h - 15 = 0

    4 +/- 14  
-------------------
        6
    
roots = 18/6 = 3
      = -10/6
        
        
x^2 - 2ax + a^2 = 0
2a +/- sqrt(4a^2 - 4a^2)
-------------------------
          2
          
          roots = a
          
          

x^2 - 4ax + 3a^2 = 0
    4a +/- 2a
-------------------
        2
         
       roots = 3a, a :)
          

x^2 - 4a^2 = 0

0 +/- 4a
-----------
      2
    
    roots = 2a, -2a

x^2 + ax - 2a^2 = 0

    a +/- 3a
---------------------
        2
        
        roots 2a, -a :))
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Surds Reminder:

(4 + sqrt(5))   (3 + sqrt(2))    12 + 4sqrt(2) + 3sqrt(5) + sqrt(10)
------------- * -------------- = ------------------------------------
(3 - sqrt(2))   (3 + sqrt(2))                     7

(8 - sqrt(3))   (9 + sqrt(3))     69 - sqrt(3)
------------- * ------------- = ----------------
(9 - sqrt(3))   (9 + sqrt(3))         78

(3sqrt(2) - 5)   (-2sqrt(7) + 6)   
-------------- * --------------- = ----------------
(2sqrt(7) + 6)    (-2sqrt(7) + 6)