Sec. 3.3 –
Quadratic equations, Functions, and Models
A quadratic equation is one equivalent to the form
2
0
ax
bx
c
+
+ =
, where a, b, and c are
real numbers, and a
≠
0.
The techniques used to solve quadratic equations are :
(1) factoring and using the zeroproduct property.
(2) getting
2
x
by itself equal a number, and using the square root of both sides.
(3) completing the square process.
(4) using the quadratic formula.
Which of the above techniques is used generally depends on the particular equation.
(1) If c = 0, there is no constant term, you can always factor out an
x
and use
technique #1.
Ex.
2
3
5
0
x
x

=
(3
5)
0
x
x

=
0
x
=
or
5
3
x
=
(2) If b = 0, there is no xterm, you can always use technique #2.
Ex.
2
6
5
0
x
 =
2
6
5
x
=
2
5
6
x
=
5
6
x
= ±
30
6
x
= ±
(3) If the three terms in the quadratic are factorable, use technique#1.
Ex.
2
12
0
x
x
 
=
(
4)(
3)
0
x
x

+
=
4
x
=
or
3
x
= 
(4) If the quadratic is not factorable, you can use technique #3 or #4. These will
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 Fall '06
 Lebre
 Algebra, Factoring, Real Numbers, Equations, Quadratic equation, real solutions

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