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Source: College Mathematics
, Rockswold G., Bennett J., and Briggs W.
C:/CLASES_COLEGIO/2007/NOTAS/0102/
02/04/07
Math 1332  College Mathematics
Chapter 32 Notes
Quadratic Equations and Problem Solving
We now focus on solving quadratic equations.
Recall we learned how to solve for linear equations
(section 23); we will also solve quadratic equations graphically, numerically, and symbolically.
Note
Æ
a quadratic equation can have zero, one, or two real solutions.
Quadratic Equation
:
A quadratic equation in one variable is an equation that can be written in the
form
ax
2
+ bx + c = 0
, where
a
,
b
, and
c
are real numbers with
a
≠
0
.
Solving Quadratic Equations
4 basic symbolic strategies:
Factoring, Square Root Property, Completing the Square, Quadratic Formula
Factoring
Æ
based on the
zeroproduct property
,
if
ab = 0
, then
a = 0
or
b = 0
or both.
Ex:
x
2
 4 = 0
Square Root Property
Æ
Let
k
be a nonnegative number.
Then the solutions to the equation
x
2
= k
are
x = ±
√
k
Ex:
x
2
 4 = 0
Æ
Completing the Square
Æ
useful when solving quadratic equations that do not factor easily!
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 Fall '11
 MariselaA.Martinez
 Linear Equations, Equations, Quadratic equation, real solutions

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