HP 15c Scientific manual Finding the Roots An Equation, Using, 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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