Texas instruments VOYAGE 200, TI-92 PLUS Polynomial Root Finder

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 Polynom ia l Complex Roots Complex Coefficient s

More Information

Customer Support Error Messages Notes and Hints

Important Information

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TI-89 / TI-92 Plus / Voyage™ 200 PLT Polynomial Root Finder App Page 2

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 3

Entering a Problem

Entering data manually

1. Start

2. Enter the degree of the polynomial. The degree must be an

3. Press ¸ to display the Coefficients screen.

4. Enter the first coefficient value. You can enter a real or

5. Press ¸ or D to go to the next coefficient.

6. Continue entering coefficient values.

the Polynomial Root Finder App and select New.

integer between 1 and 30.

complex value or an expression that resolves to a real or complex value.

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 ƒ

1:Load Coefficient s 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 ƒ

8:Clear All.

Starting a new problem

Press ƒ

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3:New Problem.

Solving Numerically

Solutions are always computed numerically, regardless of whether the Exact/Approx mode setting is

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.

Auto, Exact, or

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Solving Graphically

1. After entering coefficients, press 2 ˆ (TI-89) or

1: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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