Texas Instruments Voyage 200 Manual

2/7/02 ©2001, 2002 Texas Instruments
TI-89/TI-92 Plus/Voyage™ 200
Polynomial Root Finder
How To…
Start the Application Graph a Problem
Enter a Problem Store Values
Solve a Problem Navigate
Examples
Roots of a Third-Degree Polynomial
Complex Roots
Complex Coefficients
More Information
Customer Support Error Messages
Notes and Hints
TI

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 2
Important Information
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TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 3
What is the Polynomial Root Finder
Application?
The Polynomial Root Finder application (App) calculates numeric
roots (zeros) of polynomials using the calculator’s eigenvalue
routines.
The Polynomial Root Finder App provides a convenient,
easy-to-use interface to simplify setting up the problem, solving
it, and exploring the solution.
You can:
•Edit the coefficients of the polynomial.7
•Load a list for the coefficients.
•Store the solution in a list.
•Graph the polynomial.
•Solve up to 30th-order real or complex polynomials.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 4
Entering a Problem
Entering data manually
1. Start the Polynomial Root Finder App and select New.
2. Enter the degree of the polynomial. The degree must be an
integer between 1 and 30.
3. Press ¸to display the Coefficients screen.
4. Enter the first coefficient value. You can enter a real or
complex value or an expression that resolves to a real or
complex value.
5. Press ¸or Dto go to the next coefficient.
6. Continue entering coefficient values.
7. Press ¸after entering the last coefficient value.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 5
Loading existing data
You can load an existing list as all or part of the problem from
within the Polynomial Root Finder App by using either of the
following methods.
•Press „and select a folder and list.
•Press ƒ1:Load Coefficients and select a folder and list.
Editing coefficients
1. If you are on the Solutions screen, press †to display the
Coefficients screen.
2. Move the cursor to a coefficient and change its value.
3. Press ¸to accept the changes.
Clearing coefficients
Press ƒ8:Clear All.
Starting a new problem
Press ƒ3:New Problem.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 6
Solving Numerically
Solutions are always computed numerically, regardless of
whether the Exact/Approx mode setting is Auto,Exact,or
Approximate.The Polynomial Root Finder App calculates roots
numerically by finding the eigenvalues of a corresponding
companion matrix.
1. Complete the coefficient entry in the Coefficients screen. You
must press ¸to accept the last entered or changed
value.
2. Press ‡to solve the problem. The numeric values of the
roots appear in the Solutions screen. The busy indicator on
the status line displays while calculating the solution.
Note The roots x1...xnare displayed according to the Complex
Format mode setting. If the mode is Real,complex roots
are displayed as Non-Real unless a complex coefficient
was entered.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 7
Solving raphically
1. After entering coefficients, press 2 ˆ (TI-89) or
ˆ1:Open Graph.This option is available from either the
Coefficients or Solutions screen.
2. Select the graphing options and press ¸.
−Split Screen — Choose 1:Full or 2:Left-Right.(The
Top-Bottom option is not available.)
−Store Poly to — Choose a y-variable or choose 1:none to
graph without storing.
−Zoom — Choose 1:ZoomRoots,2:ZoomStd,3:ZoomFit,or
4:none.ZoomRoots sets the viewing window based on
the solutions found by the Polynomial Root Finder App,
relative minimums and maximums, and inflection points.
When the graph displays, the standard graph tools such as
Zoom, Trace, and Math are available on the tool bar.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 8
Displaying graph with coefficients or solutions
In split screen mode, a thick border indicates the active portion.
Press 2 a to switch between the graph and the Coefficients
or Solutions portion.
Graph portion is active Coefficients portion is active
To display the Solutions screen with the graph, switch to the
Coefficients portion of the split screen, and press ‡.
Solutions with graph
To return to the Coefficients screen, press †from the Solutions
screen.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 9
While in split screen mode, you can change the coefficients and
recalculate the solutions. The graph does not automatically
update for the new values. To update the graph, select
2 ˆ (TI-89) or ˆ1:Open Graph from the Coefficients or
Solutions screen.
Quitting the graph
1. Press 2 a to switch to the Coefficients or Solutions
screen.
2. Press 2 ˆ (TI-89) or ˆ2:Quit Graph.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 10
Storing
Once you have entered the coefficients, you can store:
•All the coefficients to a list.
•An individual coefficient to a variable.
•The polynomial to a Y= equation.
Once you have calculated the roots, you can store:
•All the roots to a list.
•An individual root to a variable.
To store from either the Coefficients or Solutions screen:
•Press …and select one of the following:
−1:Coefficients and select a folder and list name.
−2:Solutions and select a folder and list name.
−3:Poly to Y= Editor and select a y-variable.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 11
To store individual coefficients or roots from the Coefficients or
Solutions screen:
1. On the Coefficients screen, place the cursor on the value you
want to store.
On the Solutions screen, place the cursor on the equal sign
(=) of the xivalue you want to store.
2. Press §.
3. Enter a variable name and press ¸.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 12
Navigating Within the Polynomial Root Finder
App
•¤Aor ¤Bhighlights values on the Coefficients screen.
Values can be cut, copied, and pasted.
•2 A or 2 B moves the cursor to the beginning or end of
avalue on the Coefficients screen.
•2 C or 2 D moves the cursor up or down one page on
the Coefficients or Solutions screen.
•¥ C or ¥ D moves the cursor to the first or last value or
result on the Coefficients or Solutions screen.
•2 a toggles between applications or between split
screen portions.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 13
Notes and Hints
•Radian angle mode is recommended for complex number
calculations if the Complex Format mode setting is Polar.
Internally, the TI-89 / TI-92 Plus / Voyage™ 200 PLT
converts all entered trigonometry values to radians, but it
does not convert values for exponential, logarithmic, or
hyperbolic functions.
•The values of non-real roots are shown on the Solutions
screen only if the Complex Format mode setting is
Rectangular or Polar.If the format is Real, the Solutions
screen displays Non-Real.
•0is not a valid entry for an.If you press ¸on any other
coefficient without entering a value, 0 is entered
automatically. If you press ¸on anwithout entering a
value, 1 is entered automatically.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 14
Example — Roots of a Third-Degree Polynomial
Find the roots of 2x3N5x2+x+3=0.
1. Start the Polynomial Root Finder App and select New.
2. Press
3¸for a third-degree polynomial.
3. Enter the coefficients: a3=2, a2=M5, a1=1, a0=3.
4. Press ‡to solve the problem. The busy indicator on the
status line displays while the solution is calculated.
The values for x1, x2,and x3are displayed:
x1=M.618034
x2=1.5
x3=1.61803

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 15
Example — Complex Roots
Find the roots of x3+ x2+ x + 1 = 0.
1. Press 3and set Angle to Radian and Complex Format to
Real.
2. Start the Polynomial Root Finder App and select New.
3. Press
3¸for a third-degree polynomial.
4. Enter the coefficients: a3=1, a2=1, a1=1, a0=1.
5. Press ‡to solve the problem. The busy indicator on the
status line displays while the solution is calculated.
The values for x1, x2,and x3are displayed:
x1=M1.
x2=Non-Real
x3=Non-Real

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 16
Example — Complex Coefficients
Find the roots of 15 x3N4ix2+(7+i) x + 2i=0.
1. Press 3and set Angle to Radian and Complex Format to
Rectangular.
2. Start the Polynomial Root Finder App and select New.
3. Press
3¸for a third-degree polynomial.
4. Enter the coefficients: a3=15, a2=M4i, a1=7+i, a0=2i.
5. Press ‡to solve the problem. The busy indicator on the
status line displays while the solution is calculated.
The values for x1, x2,and x3are displayed:
x1=M.038274+.926765…i
x2=M.174161N.282031…i
x3=.212435N.378067…i

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 17
Errors, Error Messages, and Restrictions
Message What To Do
Highest degree
polynomial coefficient
cannot be zero.
You must enter a nonzero value for an.
All functions are in use.
Clear unnecessary
functions from the
Y= Editor.
Press ¥ # and clear any unnecessary
functions.
Memory The Polynomial Root Finder App requires
at least 3000 bytes of RAM to run properly.
When the amount of available RAM falls
below this threshold, the application may
display an Error: Memory dialog box and
return to the Home screen or simply exit to
the Home screen. If this occurs, archive or
delete some variables before returning to
the application.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 18
Installing the Polynomial Root Finder App
Detailed Flash application installation instructions are available
from education.ti.com/guides.
You will need:
•ATI-89 / TI-92 Plus / Voyage™ 200 PLT with the latest
Advanced Mathematics Software Operating System.
Download a free copy from
education.ti.com/softwareupdates.
•Acomputer using either MicrosoftëWindowsëor Appleë
Macintoshëoperating system software.
•ATI-GRAPH LINK™ computer-to-calculator cable, available
for purchase from the TI Online Store.
•Either TIConnect™ software or TI-GRAPHLINKconnectivity
software for the TI-89 / TI-92 Plus. Download a free copy
from education.ti.com/softwareupdates.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 19
Starting and Quitting the Application
Starting the Polynomial Root Finder pp
The instructions in this guidebook refer to this Flash application
only. For help using this product, refer to the comprehensive
guidebook at education.ti.com/guides.
1. Press Œand select Polynomial Root Finder.
2. Select the problem type from the menu.
−Current returns to the screen you were on when you left
the Polynomial Root Finder App.
−Open lets you select an existing list to use as the
coefficients of the polynomial.
−New creates a new problem.
Quitting the Polynomial Root Finder pp
Press 2 K from any screen.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 20
Deleting an Application
Deleting an application removes it from the handheld device and
increases space for other applications. Before deleting an
application, consider storing it on a computer for reinstallation
later.
1. Quit the application.
2. Press 2 ° to display the VAR-LINK [ALL] screen.
3. Press 2 ‰ (TI-89) or ‰to display the list of installed
applications.
4. Select the application you want to delete.
5. Press ƒ1:Delete.The VAR-LINK delete confirmation dialog
box displays.
6. Press ¸to delete the application.