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HP 39G Master Guide
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279
POLYROOT([coeff1,coeff2,…])
This function returns the roots of the
polynomial whose coeffici
ents are specified.
The coefficients must be
input as a vector in
square brackets.
Eg.
Using our earlier function of
3
()
(
2
)
(
3
)
(
1
)
7
6
fx
x
x
x
x
x
=
−+
−
=
−
+
we
can enter the coefficients as [1,0,-7,6].
As you can see in the screen shot, t
he roots of 2,
-3 and 1 have been
correctly found.
278
280
Table of Contents
Default Chapter
2
Table of Contents
2
Introduction
12
How to Use this Manual
13
Early High School
13
Pre-Calculus
14
Calculus
14
Where's the on Button
15
Some Keyboard Examples
16
Keys & Notation Conventions
17
Some Essential Keys
17
The SHIFT Key
17
The ALPHA Key
18
The Screen Keys
18
Pop-Up Menus & Short-Cuts
18
Everything Revolves Around Aplets
21
Some Typical Aplet Views
22
The HOME View
25
What Is the HOME View
25
Exploring the Keyboard
26
The Screen Keys
26
Aplet Related Keys
26
The Arrow Keys
26
The SYMB, PLOT and NUM Keys
27
Intro to the VIEWS Menu
28
The VARS Key
28
The SETUP Views
30
The MODES View
30
Numeric Formats
31
The ANS Key
32
The Negative Key
33
The CHARS Key
33
The del and CLEAR Keys
34
Angle and Numeric Settings
35
Memory Management
37
The MEMORY MANAGER View
37
Downloaded Aplets & Memory
38
The GRAPHICS MANAGER
39
The LIBRARY MANAGER
39
Fractions on the Hp 39G
40
Pitfalls to Watch for
42
The HOME History
43
Copying Calculations
43
Clearing the History
44
Showing Results
44
Storing and Retrieving Memories
45
Referring to Other Aplets from the HOME View
46
An Introduction to the MATH Menu
47
Resetting the Calculator
48
Soft Reboot
48
Soft Reboot (Hardware)
49
Hard Reboot (with Memory Wipe)
49
Summary
50
The Function Aplet
51
Choose the Aplet
51
The SYMB View
52
The Xtθ Button
52
Ing Your Function
52
The NUM View
53
The PLOT View
53
Auto Scale
54
The PLOT SETUP View
55
Detail Vs. Faster
55
Simultaneous
56
Connect
56
Axes
56
Labels
56
Grid
56
The Default Axis Settings
57
The Bar
57
The MENU Toggle
57
The Menu Bar Functions
58
Trace
58
Defn
58
Goto
59
The Zoom Sub-Menu
60
Center
60
In/Out
60
Box
61
X-Zoom In/Out X4 and Y-Zoom In/Out X4
62
Square
62
Auto Scale, Decimal, Integer and Trig
62
The FCN Menu
63
Root
63
Intersection
64
Slope
64
Signed Area
65
Definite Integrals
65
Tracing the Integral in PLOT
66
Areas between and under Curves
67
Extremum
68
Tips & Tricks - Function
69
Finding a Suitable Set of Axes
69
Composite Functions
71
Using Functions in the HOME View
72
Differentiating
73
Circular Functions
74
Trig Functions
76
Retaining Calculated Values
77
The NUM View Revisited
77
Zoom
78
Function
80
Integration: the Algebraic Indefinite Integral
81
The Hp 40G Computer Algebra System
82
Integration: the Definite Integral Using PLOT Variables
83
Piecewise Defined Functions
85
Nice' Scales
86
Use of Brackets in Functions
87
Problems When Evaluating Limits
88
Gradient at a Point
90
Finding and Accessing Polynomial Roots
91
The VIEWS Menu
92
Plot-Detail
93
Plot-Table
94
Overlay Plot
95
Auto Scale
96
Decimal, Integer & Trig
97
Downloaded Aplets from the Internet
99
Curve Areas
99
Linear Programming
99
The Parametric Aplet
100
Choose Xrng, Yrng & Trng
100
The Effect of Trng
101
Tstep Controls Smoothness
101
Tips & Tricks - Parametric Equations
103
Fun and Games
103
Example 1
103
Example 2
103
Vectors
104
Example 1
104
Example 2
105
The Polar Aplet
106
Choose Xrng, Yrng & Θrng
106
Θstep and Smoothness
106
Changing the Default for Θstep
106
Circular Circles
106
The Sequence Aplet
107
Recursive or Non-Recursive
107
First, Second & General Terms
107
Convenient Screen Keys Provided
108
Tips & Tricks - Sequences & Series
110
Defining a Generalized GP and the Sum to N Terms
110
Solving Sequence Problems
110
Modeling Loans
112
The Solve Aplet
113
Equations Vs. Expressions
113
Entering the Equation
113
Solving for a Missing Value
114
The INFO Report
114
Multiple Solutions and the Initial Guess
115
Graphing in Solve
116
Transferring Approximate Solutions
116
Referring to Functions from Other Aplets
117
A Detailed Explanation of PLOT in Solve
118
The Meaning of Messages
120
Tips & Tricks - Solve
121
Easy Problems
121
Harder Problems
121
The Stats Aplet - Univariate Data
122
Uni Vs. Bi-Variate Data
122
Clearing Data
122
Sorting Data
123
The STATS Key
123
Functions of Columns
124
Registering Columns as 'In Use
124
Working with Frequency Tables
125
Auto Scale
125
Plot Setup Options
126
Box and Whisker Graphs
126
The Effect of Hrng
127
Grouped Data & Hwidth
127
Tips & Tricks - Univariate Data
129
New Columns as Functions of Old
129
Simulating Dice
129
Simulating Random Variables
130
The Stats Aplet - Bivariate Data
132
Uni Vs. Bi-Variate Data
132
Clearing Data
132
Entering Data as Ordered Pairs
133
Adjusting the Symbols Used to Plot Points
133
The Cursor
133
Sorting Paired Columns
134
Specifying the Fit Model
134
Multiple Data Sets
134
Choosing from Available Fit Models
135
The User Defined Model
135
Connected Data
136
Two Variable Statistics
137
Showing the Line of Best Fit
138
Predicting Using PREDY
140
Predicting Using the PLOT View
140
Relerr as a Measure of Non-Linear Fit
141
Tips & Tricks - Bivariate Data
143
New Columns as Functions of Old
143
Using Values from in Calculations
143
Obtaining Coefficients from the Fit Model
145
Finding Fit Coefficients
145
Correct Interpretation of the PREDX Function
146
Assigning Rank Orders to Sets of Data
147
Using Stats to Find Equations from Point Data
148
The Inference Aplet
150
Using the Chi2 Test on a Frequency Table
150
Hypothesis Test: T-Test 1-Μ
151
Confidence Interval: T-Int 1-Μ
153
Hypothesis Test: T-Test Μ
154
Hypothesis Test: Z-Test 1-Μ
156
Tips & Tricks - Inference
158
Importing from a Frequency Table
158
The Finance Aplet
160
Parameters
160
Straightforward Compound Interest
161
Annuity
162
Loan Calculations
162
Amortization
163
The Quad Explorer Teaching Aplet
164
Objectives
164
Choosing the Level
164
GRAPH Mode
164
SYMB Mode
165
Self Test Mode
166
The Trig Explorer Teaching Aplet
167
Objectives
167
SIN Vs. COS
167
SYMB Vs. GRPH Mode
167
Using Matrices on the Hp 39G
170
The MATRIX Catalog
170
Matrix Calculations in the HOME View
171
Solving a System of Equations
172
Finding an Inverse Matrix
174
The Dot Product
175
Using Lists on the Hp 39G
176
The List Variables
176
Operations on Lists
176
Statistical Columns as Lists
176
List Functions
177
Editing a List
177
Operations on Elements
177
Using the Notepad Catalog
178
Aplet Notes Vs. Independent Notes
178
Independent Notes and the Notepad Catalog
179
Transferring Notes Using IR
180
Editing Software
180
Software
181
For the Hp 38G, Hp 39G & Hp 40G
181
For the Hp 39G
181
Creating a Note
182
Locking ALPHA Mode
182
The CHARS View
183
Corrupting Notes
183
Using the Aplet Sketchpad
184
Adding Text to a Sketch
184
The DRAW Menu
185
Dot
185
Line
185
Box
185
Circle
186
Cut and Paste (Sort of
186
Capturing the PLOT Screen
187
Using, Copying & Creating Aplets
189
Creating a Copy of a Standard Aplet
190
Copying and Adding to the Function Aplet
190
Copying and Adding to the Stats Aplet
191
Some Examples of Saved Aplets
192
The Triangles Aplet
192
The Prob. Distributions Aplet
192
The Transformer Aplet
194
Copying from Hp 39G+ to Hp 39G+ Via the Infra-Red Link
197
The Infra-Red Port
197
Time out
199
Attached Programs
199
Downloading Aplets from the Internet
200
Finding Aplets
200
Organizing Your Collection
201
Software for the Hp 38G, Hp 39G & Hp 40G
202
Software for the Hp 39G
203
The Hpgcomm Connectivity Program
204
Deleting Downloaded Aplets from the Calculator
207
Saving Notes, Aplets and Sketches Via the Connectivity Kit
208
Capturing Screens Using the Connectivity Kit
210
Editing Notes with the Aplet Development Kit
211
Programming the Hp 39G
212
The Design Process
212
An Overview
212
Choosing the Parent Aplet
212
Naming Conventions
213
Planning the VIEWS Menu
214
The SETVIEWS Command
214
Special Entries in the SETVIEWS Command
216
The 'Start' Entry
217
Example Aplet #1
217
Example Aplet #2
222
Example Aplet #3
224
Example Aplet #4
226
Programming Commands
233
The Aplet Commands
233
Check & Uncheck
233
Select
233
Setviews
234
The Branch Commands
234
If then [Else] End
234
Case
234
Ifferr then [Else] End
234
Run
235
Stop
235
The Drawing Commands
235
Arc
235
Box
235
Erase
236
Freeze
236
Line
236
PIXON and PIXOFF
236
Tline
236
The Graphics Commands
237
The Loop Commands
237
FOR <Var> = <Start> to <End> [STEP] <Statements> END
237
Do until
237
While Repeat
237
Break
238
The Matrix Commands
238
Editmat
238
Redim
238
The Print Commands
239
Prdisplay
239
Prhistory
239
Prvar
239
The Prompt Commands
240
Beep
240
Choose
240
Disp
241
Dispxy
241
Disptime
241
Getkey
241
Input
242
Msgbox
242
Prompt
242
Wait
242
The MATH Menu Functions
243
The 'Real' Group of Functions
246
Ceiling
246
Deg Rad
246
Floor
246
Fnroot
247
Frac
247
Hms Hms
248
Int
249
Mant
249
Max
249
Min
250
Mod
250
Change
251
Total
251
Rad Deg
251
Round
252
Sign
252
Truncate
253
Xpon
253
The 'Stat-Two' Group of Functions
254
Predy
254
Predx
254
The 'Symbolic' Group of Functions
255
The = 'Function
255
Isolate
255
Linear
256
Quad
256
Quote
257
The | Function
258
The 'Tests' Group of Functions
259
The 'Trigonometric' & 'Hyperbolic' Groups of Functions
259
COT, SEC Etc
259
Exp
260
Alog
260
Expm1
260
Lnp1
261
The 'Calculus' Group of Functions
261
The 'Complex' Group of Functions
262
Abs
263
Sign
263
Arg
264
Conj
264
IM & Re
264
The 'List' Group of Functions
265
Concat
265
List
266
Makelist
266
Πlist
267
Pos
267
Size
268
Σlist
268
Reverse
268
Sort
268
The 'Loop' Group of Functions
269
Iterate
269
Recurse
270
Σ (Summation)
270
The 'Matrix' Group of Functions
271
Colnorm
271
Cond
271
Cross
271
Det
272
Dot
272
Eigenval
272
Eigenvv
272
Identmat
272
Inverse
273
Lsq
274
Makemat
274
Rank
274
Rownorm
274
Rref
274
Schur
275
Size
275
Specnorm
275
Specrad
275
Svd
275
Svl
275
Trace
276
Trn
276
The 'Polynomial' Group of Functions
277
Polycoef
277
Polyeval
277
Polyform
278
Polyroot
279
The 'Probability' Group of Functions
280
Comb
280
The ! Function
280
Perm
281
Random
281
Randseed
281
Utpn
282
Utpc
283
Utpf
283
Utpt
283
Appendix A: Worked Examples
284
Finding the Intercepts of a Quadratic
284
Method 1 - Using the QUAD Function in HOME
284
Method 2 - Using the Function Aplet
284
Method 3 - Using the POLYROOT Function
285
Finding Complex Solutions to a Complex Equation
285
Method 1 - Using the QUAD Function
285
Method 2 - Using POLYROOT
285
Finding Critical Points and Graphing a Polynomial
286
Solving Simultaneous Equations
288
Method 1 - Graphing the Lines
288
Second Method - Using a Matrix
288
Third Method - Using the 3X3 Solver Aplet
289
Expanding Polynomials
290
Exponential Growth
291
Solution of Matrix Equations
293
Inconsistent Systems of Equations
294
Using the RREF Function
294
Finding Complex Roots
295
Analyzing Vector Motion and Collisions
296
Circular Motion and the Dot Product
297
Inference Testing Using the Chi 2 Test
299
Appendix B: Teaching Calculus with an Hp 39G
301
Investigating y X = N for N an Integer
301
Investigating y X= for N an Integer
302
Domains and Composite Functions
302
Gradient at a Point
303
Gradient Function
304
The Chain Rule
305
Optimization
305
Area under Curves
306
Fields of Slopes and Curve Families
306
Inequalities
307
Rectilinear Motion
307
Limits
307
Piecewise Defined Functions
308
Sequences and Series
308
Transformations of Graphs
309
Appendix C: the Hp 40G & Its CAS
310
Introduction
310
What Is a CAS
310
What Is the Difference between the Hp 39G, Hp 40G & Hp 39G
312
Using the CAS
313
Entering and Editing an Expression
313
In-Line Editing Mode
316
Erasing, Copying, Cutting and Pasting
316
Cursor Mode
317
The CAS HOME History
317
The PUSH and POP Commands
318
Pasting to an Aplet
319
Evaluating Algebraic Expressions
320
Using Functions in the CAS
321
E.g. 1 Using LIMIT
321
E.g. 2 Factorizing Expressions
322
E.g. 3 Solving Equations
323
E.g. 4 Solving Simultaneous Equations
323
E.g. 5 Solving a Simultaneous Integration
325
E.g. 6 Defining a User Function
327
On-Line Help
328
Configuring the CAS
329
Tips & Tricks - CAS
330
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HP 39G Specifications
General
Brand
HP
Model
39G
Category
Calculator
Language
English
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