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
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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.