HP 15c Collector's Edition User Manual

Section 13: Finding the Roots of an Equation 181
The basic rules for using _ are:
1. In Program mode, key in a subroutine that evaluates the function
f(x) that is to be equated to zero. This subroutine must begin with a
label instruction (´ b label) and end up with a result for f(x)
in the X-register.
In Run mode:
2. Key two initial estimates of the desired root, separated by v,
into the X- and Y-registers. These estimates merely indicate to the
calculator the approximate range of x in which it should initially
seek a root of f(x) = 0.
3. Press ´ _ followed by the label of your subroutine. The
calculator then searches for the desired zero of your function and
displays the result. If the function that you are analyzing equals
zero at more than one value of x, the routine will stop when it finds
any one of those values. To find additional values, you can key in
different initial estimates and use _ again.
Immediately before _ addresses your subroutine it places a value
of x in the X-, Y-, Z-, and T-registers. This value is then used by your
subroutine to calculate f(x). Because the entire stack is filled with the x-
value, this number is continually available to your subroutine. (The use of
this technique is described on page 41).
Example: Use _ to find the values of x for which
f(x) = x
2
− 3x − 10 = 0.
Using Horner’s method (refer to page 79), you can rewrite f(x) so that it is
programmed more efficiently:
f(x) = (x − 3)x − 10.
In Program mode, key in the following subroutine to evaluate f(x).
Keystrokes Display
| ¥
000-
Program mode.
´ CLEAR M
000-
Clear program memory.

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.