HP 15c Collector's Edition User Manual

Section 13: Finding the Roots of an Equation 187
Because the absolute-value function is minimum near an argument of
zero, specify the initial estimates in that region, for instance 1 and −1.
Then attempt to find a root.
Keystrokes Display
| ¥ Run mode.
1 v
1.0000
Initial estimates.
1 ”
-1
´ _ 1
Error 8
This display indicates that
no root was found.
−
0.0000
Clear error display.
As you can see, the HP 15c stopped seeking a root of f (x) = 0 when it
decided that none existed—at least not in the general range of x to which
it was initially directed. The Error 8 display does not indicate that an
“illegal” operation has been attempted; it merely states that no root was
found where _ presumed one might exist (based on your initial
estimates).
If the HP 15c stops seeking a root and displays an error message, one of
these three types of conditions has occurred:
 If repeated iterations all produce a constant nonzero value for the
specified function, execution stops with the display Error 8 .
 If numerous samples indicate that the magnitude of the function
appears to have a nonzero minimum value in the area being
searched, execution stops with the display Error 8 .
 If an improper argument is used in a mathematical operation as part
of your subroutine, execution stops with the display Error 0 .
In the case of a constant function value, the routine can see no indication
of a tendency for the value to move toward zero. This can occur for a
function whose first 10 significant digits are constant (such as when its
graph levels off at a nonzero horizontal asymptote) or for a function with
a relatively broad, local “flat” region in comparison to the range of x-
values being tried.
In the case where the function’s magnitude reaches a nonzero minimum,
the routine has logically pursued a sequence of samples for which the
magnitude has been getting smaller. However, it has not found a value of
x at which the function’s graph touches or crosses the x-axis.

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.