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.
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