1
MA 15200
Lesson 14
Section 1.5 (part 1)
The
general form
of a
quadratic equation
is
2
0
ax
bx
c
+
+ =
, where
a, b,
and
c
are real
numbers and
0
a
≠
.
This is a second degree equation.
There are four ways to possibly solve quadratic equations.
1.
Solving by Factoring
2.
Solving by the Square Root Property
3.
Solving by Completing the Square
4.
Solving with the Quadratic Formula
I
Solving by Factoring
ZeroProduct Principle:
If the product of two algebraic expressions is zero, then at
least one of the factors is equal to zero.
If
0, then
0 or
0.
AB
A
B
=
=
=
Steps:
1.
If necessary, rewrite the equation in general form (zero on one side, polynomial in
descending order).
2.
Factor the polynomial completely.
3.
Apply the zeroproduct principle, setting each factor containing a variable equal
to zero.
4.
Solve the resulting equations.
Ex 1:
Solve by using factoring.
2
2
2
2
)
28 3
)
121
0
)
3
30
0
)
5
12
2
a
x
x
b
x
c
x
x
d
x
x
=


=
+
=
+
=
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If a quadratic equation can be solved by factoring, the solution(s) is(are)
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 Fall '09
 Real Numbers, Equations, Quadratic equation, square root property

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