HP 15c Collector's Edition User Manual

184 Section 13: Finding the Roots of an Equation
You have now found the two roots of
f(x) = 0. Note that this quadratic equation
could have been solved algebraically—
and you would have obtained the same
roots that you found using _.
The convenience and power of the _ key become more apparent
when you solve an equation for a root that cannot be determined
algebraically.
Example: Champion ridget hurler Chuck
Fahr throws a ridget with an upward
velocity of 50 meters/second. If the height
of the ridget is expressed as
h = 5000(1 − e
−t / 20
) − 200t,
how long does it take for it to reach the
ground again? In this equation, h is the
height in meters and t is the time in
seconds.
Solution: The desired solution is the
positive value of t at which h = 0.
Use the following subroutine to calculate the height.
Keystrokes Display
| ¥
000-
´ b A
001-42,21,11
Begin with label.
2
002- 2
Subroutine assumes t is
loaded in X- and Y-registers.
0
003- 0
÷
004- 10
Graph of f (x)

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.