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Solving Quadratic Equations

Complete the table and then make the observations listed below.

Expanded form equations Factored form equations Equations Solutions
x2+ 6x - 16 = 0 (x + 8) (x-2) = 0 x + 8 = 0
x – 2 = 0
-8 or 2
x2 - 8x - 20 = 0 (x + 2) (x-10) = 0 x + 2 = 0
x - 10 =
 
x2 + 10x +21 = 0 (x + 7) ( ) = 0 x + 7 = 0
x + 3 =
 
x2 + 4x + 3 = 0 (x + ) (x + ) = 0 x + 3
x +
 
x2 + 5x + 6 = 0 (x + ) (x + ) = 0    
x2 - 7x + 10 = 0 (x - ) (x - ) = 0    
x2 - 7x + 12 = 0 ( ) ( ) = 0    
x2 - x - 12 = 0 ( ) ( ) = 0    
x2 + x - 12 = 0 ( ) ( ) = 0    
x2 + 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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