180
Section 13
Finding the Roots
of an Equation
In many applications you need to solve equations of the form
f(x)=
0
.
*
This means finding the values of
x
that
satisfy the equation. Each such value
of
x
is called a
root
of the equation
f(x)
= 0 and a
zero
of the function
f(x).
These roots (or zeros) that are real
numbers are called
real
roots
(or real
zeros). For many problems the roots of
an equation can be determined
analytically
through
algebraic
manipulation; in many other instances,
this is not possible. Numerical
techniques can be used to estimate the
roots when analytical methods are not suitable. When you use the
_
key on your HP-15C, you utilize an advanced numerical technique that lets
you effectively and conveniently find
real roots
for a wide range of
equations.
†
Using
_
In calculating roots, the
_
operation repeatedly calls up and executes
a subroutine
that you write
for evaluating
f(x).
*
Actually,
any
equation with one variable can be expressed in this form. For example,
f(x)
= a
is equivalent
to
f(x) – a
= 0, and
f(x)
= g(
x
) is equivalent to
f(x)
–
g
(
x
) = 0.
†
The
_
function does not use the imaginary stack. Refer to the
HP-15C
Advanced Functions
Handbook
for information about complex roots.
Содержание HP-15C
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