HP 15c - Manual (Page 12)

12 Section 1: Using _ Effectively
12
In general, every equation is one of an infinite family of equivalent equations with the same
real roots. And some of those equations must be easier to solve than others. While _
may fail to find a root for one of those equations, it may succeed with another.
Inaccurate Equations
_ can't calculate an equation's root incorrectly unless the function is incorrectly
calculated. The accuracy of your function subroutine affects the accuracy of the root that you
find.
You should be aware of conditions that might cause your calculated function value to differ
from the theoretical value you want it to have.
_ can't infer intended values of your
function. Frequently, you can minimize calculation error by carefully writing your function
subroutine.
Equations With Several Roots
The task of finding all roots of an equation becomes more difficult as the number of roots
increases. And any roots that cluster closely will usually defy attempts at accurate resolution.
You can use deflation to eliminate roots, as described in the HP-15C Owner's Handbook.
An equation with a multiple root is characterized by the function and its first few higher-
order derivatives being zero at the multiple root. When
_
finds a double root, the last
half of its digits may be inaccurate. For a triple root, two-thirds of the root's digits tend to be
obscured. A quadruple root tends to lose about three-fourths of its digits.
Using
_ With Polynomials
Polynomials are among the easiest functions to evaluate. That is why they are traditionally
used to approximate functions that model physical processes or more complex mathematical
functions.
A polynomial of degree n can be represented as
a
n
x
n
+ a
n−1
x
n−1
+ … + a
1
x + a
0
.