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Math 1310 Class Notes – Section 2.3, Page 1 of 6
Math 1310
Section 2.3
Quadratic Equations
In this section, you’ll learn three methods for solving quadratic equations.
A quadratic
equation is an equation of the form
0
2
=
+
+
c
bx
ax
, where
0
≠
a
.
Equations of this form
can have two solutions, one solution or no solutions.
•
Factoring
The first method you can use is factoring.
This method makes use of the Zero Product
Property, that is, if
0
=
ab
, then either
a
= 0 or
b
= 0.
The equation must be written in the form
0
2
=
+
+
c
bx
ax
, so you may have to rewrite the
equation in this form before you get started.
Next you’ll factor the left hand side of the
equation.
Once in factored form, you’ll use the Zero Product Property to solve the
equation.
Example 1:
Solve for
x
:
0
14
5
2
=


x
x
Example 2:
Solve for
x
:
12
)
4
(
=

x
x
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Example 3:
Solve for
x
:
0
10
17
3
2
=
+

x
x
Example 4:
Solve for
x
:
0
81
25
2
=

x
Sometimes you’ll want to look for a common factor before proceeding as we did on the
first four examples.
Example 5:
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This note was uploaded on 02/22/2012 for the course MATH 1310 taught by Professor Marks during the Summer '08 term at University of Houston.
 Summer '08
 MARKS
 Equations

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