Solving Quadratic Equations
Complete the table and then make the observations listed below.
Expanded form equations  Factored form equations  Equations  Solutions 
x^{2}+ 6x  16 = 0  (x + 8) (x2) = 0  x + 8 = 0 x – 2 = 0 
8 or 2 
x^{2}  8x  20 = 0  (x + 2) (x10) = 0  x + 2 = 0 x  10 = 

x^{2} + 10x +21 = 0  (x + 7) ( ) = 0  x + 7 = 0 x + 3 = 

x^{2} + 4x + 3 = 0  (x + ) (x + ) = 0  x + 3 x + 

x^{2} + 5x + 6 = 0  (x + ) (x + ) = 0  
x^{2}  7x + 10 = 0  (x  ) (x  ) = 0  
x^{2}  7x + 12 = 0  ( ) ( ) = 0  
x^{2}  x  12 = 0  ( ) ( ) = 0  
x^{2} + x  12 = 0  ( ) ( ) = 0  
x^{2} + 7x + 12 = 0  ( ) ( ) = 0 
Look at the Factored form equations and your solutions .
Can you see a pattern?
What can you say about the factored form if the solutions are both positive ?
What can you say about the factored form if the solutions are both negative ?
What can you say about the factored form if the solutions are negative and
positive ?
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