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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.
îš‚
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.
îš‚
The _ function does not use the imaginary stack. Refer to the HP-15C Advanced Functions
Handbook for information about complex roots.
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