Unit 8  Objective 1  Quadratic Equations  Solution by
Factoring
A polynomial equation of the second degree is called a quadratic equation.
If a, b, and c are constants and a 0, then
ax^{2} + bx + c = 0
is the general quadratic equation. The following are quadratic equations:
1.  x^{2} = 5 x^{2}  5 = 0 a = 1, b = 0, c = 5 
2.  3x^{2}  x + 5 = 0 a= 3, b = 1, c = 5 
3.  x^{2} = x x^{2}  x = 0 a =  1, b =  1, c = 0 
The following are not quadratic equations:
1.  4x = 5 
(There is not a x^{2} term) 
2.  x^{3} + x^{2}  x + 2 = 0  (There should not be any terms with a degree higher than 2) 
As you solve quadratic equations we need to know the zero principle: if a and b are
numbers and ab = 0 then a=0, b=0 or both a and b are 0. To find roots, make sure the equation equals 0 to use the zero principle.
Examples:

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