1/6/2010
1
Problem:
A room is 4m longer than it is wide. The area or the room is
20m
2
. What is the area of the room?
Let
x
be the width of the room.
Then the area of the room is
x
(
x
+ 4) =
x
2
+ 4x
Equating this to the given area gives
x
2
+ 4x = 20
Rearranging gives
x
2
+ 4x–20 = 0
This is a “root finding” problem.
Root Finding Problems:
•
General form: find
x
such that
f
(
x
) = 0
•
The values of
x
for which
f
(
x
) = 0 are the
roots
of
f
(
x
)
c
bx
ax
x
f
)
(
2
For our problem
f
(
x
) happens to be a
quadratic
.
The roots can be found using the quadratic formula.
a
ac
b
b
x
x
roots
2
4
,
2
2
1
In general there are two roots.
One is obtained by using + in the formula and the other by using
‐
.
If the quantity under the square root is zero the roots are equal.
If this quantity is negative the roots are complex numbers.
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2
Casio Calculator Note
Casio calculators can solve quadratics.
Hit
Mode
until menu include “EQN”. Then select this option.
Use the right arrow to move from “Unknowns?” to “Degree?”
Enter 2 (a quadratic is a second degree polynomial)
Enter values for
a
,
b
, and
c
(hit “=“ after each value)
Use the up and down arrows to move between the two solutions.
If the roots are complex numbers
shift
plus “=“ toggles between the real and
imaginary parts of each solution. If the roots are real this key combination has
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 Winter '09
 editor, @, Complex number, 4m

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