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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