HP 15c Collector's Edition User Manual

234 Appendix D: A Detailed Look at _
lines should subtract the known root (to 10 significant digits) from the x-
value and divide this difference into the function value. In many cases the
root will be a simple one, and the new function will direct _ away
from the known root.
On the other hand, the root may be a multiple root. A multiple root is one
that appears to be present repeatedly, in the following sense: at such a
root, not only does the graph of f (x) cross the x-axis, but its slope (and
perhaps the next few higher-order derivatives) also equals zero. If the
known root of your equation is a multiple root, the root is not eliminated
by merely dividing by the factor described above. For example, the
equation
f (x) = x(x − a)
3
= 0
has a multiple root at x = a (with a multiplicity of 3). This root is not
eliminated by dividing f (x) by (x − a). But it can be eliminated by dividing
by (x − a)
3
.
Example: Use deflation to help find the roots of
60x
4
− 944x
3
+ 3003x
2
+ 6171x − 2890 = 0.
Using Horner’s method, this equation can be rewritten in the form
{[(60x − 944)x + 3003]x + 6171}x − 2890 = 0.
Program a subroutine that evaluates the polynomial.
Keystrokes
Display
| ¥
000-
Program mode.
´ CLEAR M
000-
´ b 2
001-42,21, 2
6
002- 6
0
003- 0
*
004- 20
9
005- 9
4
006- 4
4
007- 4
-
008- 30
*
009- 20
3
010- 3
0
011- 0

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.