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62
L8
§2.4 Quadratic Equations
The
quadratic equation
is an equation that can be
written in the form
2
0
ax
bx
c
+
+=
where
a, b,
and
c
are real numbers and
0
a
≠
.
Solving by factoring
ZeroFactor Property
:
If
0
ab
=
, then
0
a
=
, or
0
b
=
, or both.
This property can be applied to more than two factors.
Important:
Always set an equation of degree 2 or
higher equal to zero before applying the
ZeroFactor
property
.
Example
:
Solve
2
31
8
2
1
x
x
+
=
.
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Example
:
Solve
3
4
x
x
=
.
Square Root Property
:
The solution set to
2
x
k
=
is
x
k
= ±
.
Note
:
If
0
k
≥
,
k
is the principle square root (nonnegative).
If
0
k
<
,
ki
k
=−
(imaginary number).
Example
. Solve each quadratic equation:
a)
2
32
x
b)
2
(3
)4
9
z
−=
64
Completing the Square
:
We can solve a quadratic equation
2
0(
0
)
ax
bx
c
a
++
=
≠
by
completing the square
.
Steps
(must be memorized)
:
1.
Make sure that
1
a
=
; if not, divide each term by
a
.
2.
Get the constant on the right side of the equation.
3.
Take 1/2 of the coefficient of
x
and square it.
4.
Add this number to both sides of the equation.
5.
Factor the lefthand side into a perfect square.
6.
Solve for
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This note was uploaded on 02/29/2012 for the course MAC 1140 taught by Professor Gregory during the Fall '11 term at Broward College.
 Fall '11
 gregory
 Factoring, Real Numbers, Equations

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