Texas Instruments TI-83 Plus Silver Edition Manual
7/31/01 ©2001 Texas Instruments
TI-83 Plus Polynomial Root
Finder & Simultaneous
Equation Solver Application
Getting Started
Polynomial Root Finder – Precalculus Level Example
Polynomial Root Finder – Calculus Level Example
Simultaneous Equation Solver
How To…
Load Values from a List Load Values from a Matrix
Store Data into Lists Store Data into Matrices
Examples
Finding the Roots of a Polynomial
Solving a System of Equations
Displaying a Matrix in Reduced Row-Echelon Form
More Information
Customer Support Error Recovery
TI
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 2
Important Information
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implied, including but not limited to any implied warranties of
merchantability and fitness for a particular purpose, regarding
any programs or book materials and makes such materials
available solely on an "as-is" basis.
In no event shall Texas Instruments be liable to anyone for
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Instruments, regardless of the form of action, shall not exceed
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Texas Instruments shall not be liable for any claim of any kind
whatsoever against the use of these materials by any other
party.
Graphing product applications (Apps) are licensed. See the
terms of the license agreement for this product.
TI-GRAPH LINK and TI-Cares are trademarks of Texas Instruments. All other trademarks
are the property of their respective owners.
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 3
What Is the Polynomial Root Finder &
Simultaneous Equation Solver Application?
The Polynomial Root Finder application calculates the roots
(zeros) of polynomials of degree 1 through 30, with a convenient,
easy to use interface. You can store solutions into lists, load lists
into the application for editing, and graph the polynomial.
Because the application uses the operating system’s eigenvalue
routines, solutions are computed numerically only.
The Simultaneous Equation Solver application finds solutions to
systems of linear equations. You can load matrices containing
the coefficients of linear systems and identify whether a given
system has a unique solution, an infinite number of solutions, or
no solution.
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 4
What You Need to Install and Use the Application
To install and run the application, you need:
•A TI-83 Plus calculator with version 1.13 or later of the
operating system software to optimize the performance of your
calculator and the application.
-To check the operating system version, press \/,
and then select About. The version number is displayed
below the product name.
-You can download a free copy of the latest operating
system software from education.ti.com/softwareupdates.
Follow the link to Operating Systems.
•A computer with WindowsÍ95/98/2000, Windows NTÍ, or
Apple® Mac® OS 7.0 or later installed.
•A TI-GRAPH LINK™ computer-to-calculator cable. If you do
not have this cable, call your distributor, or order the cable
online from TI's online store.
•TI-GRAPH LINK software that is compatible with the
TI83 Plus. You can download a free copy of the
TI-GRAPH LINK software from
education.ti.com/softwareupdates. Follow the link to
Connectivity Software, then TI-GRAPH LINK.
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 5
Where to Find Installation Instructions
Detailed installation instructions are available from
education.ti.com/guides. Follow the link to Flash installation
instructions.
Getting Help
This application contains built-in help screens that give you
information about how to use both the Polynomial Root Finder
and the Simultaneous Equation Solver applications. To access
and use the help screens:
1. From the
MAIN MENU, select either Poly Help or Simult Help.
2. Press
ato display subsequent screens.
3. Press
\to exit the help screens and return to the
MAIN MENU.
Press \to
exit the help
screens and return
to the Main Menu.
Press ato view
the next help
screen.
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 6
Polynomial Root Finder Application
Getting Started with the Polynomial Root Finder Application
Precalculus Level Example
Work through the following example to get acquainted with the
main features of the Polynomial Root Finder application.
A golfer hits a golf ball from a tee at the bottom of a hill. The
hill can be described by y(x) = .8x. The ball follows the path
y(x) = 0x2+12x. If the golfer is standing at the tee (0,0) and
hits the ball, where does the ball hit the ground on the hill?
To solve this problem, you need to find where the path of the
golf ball, y(x) = 0x2+12x, will hit the hill, y(x) = .8x. Solve this
by hand first, and then follow the instructions below to verify
your calculation.
hill
path of the
golf ball
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 7
1. First, equate the two equations.
0x2+12x = .8x
0x2+11.2x = 0
The roots of the resulting polynomial will give the intersection
points of the ball path and the hill.
2. Press
nto display a list of applications on your calculator.
3. Select
PolySmlt. The information screen is displayed.
4. Press any key to continue. The MAIN MENU is displayed.
5. Select
Poly Root Finder.
6. Enter the degree of the polynomial (2), and then press ¯.
7. Enter the coefficients of the polynomial {01, 11.2, 0}. Press
¯after each coefficient to move the cursor to the next
line.
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 8
8. Select
SOLVE (press V) to calculate and display the
roots.
Two answers, x1=11.2 and x2=0, are displayed. If you exit the
application, graph the two functions, and find their intersection
(press \, and then select Intersect), you can see that the
ball starts at (0,0) and hits the hill at (11.2, 8.96).
To see this graph:
1. Press T
2. Select Zoom Out.
3. Move the cursor near (0,0).
4. Press ¯.
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 9
Calculus Level Example
Work through the following example to get acquainted with the
main features of the Polynomial Root Finder application.
An open box is to be made from a square piece of material 36
centimeters on a side by cutting equal squares from the
corners and turning up the sides. What is the largest volume
box that can be made with this construction?
L = (36 – 2x)
W=(36 – 2x)
H=x
The volume of the box is V(x) = x(36-2x)2.
36 cm
x
36 –2x cm
TI-83 Plus Polynomial Root Finder / Simultaneous Equation Solver Application Page 10
1. To find the extreme values of the volume, set the first
derivative of V to zero.
V(x) = x(36-2x)2
V(x) = 4x3–144x2+1296x
V'(x) = 12x2–288x + 1296 = 0
x2–24x + 108 = 0
2. Now, if you find the roots of x2–24x + 108 = 0, you will find
the critical points of the function.
3. Press
nto display a list of applications on your calculator.
4.Select PolySmlt. The information screen is displayed.
5. Press any key to continue. The MAIN MENU is displayed.
6. Select
Poly Root Finder.
7. Enter the degree of the polynomial (2), and then press ¯.
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