HP 15c Scientific manual Finding the Roots of an Equation, Clear program memory

Section 13: Finding the Roots of an Equation 181

The basic rules for using _are:

1.In Program mode, key in a subroutine that evaluates the function f(x) that is to be equated to zero. This subroutine must begin with a label instruction (´b label) and end up with a result for f(x) in the X-register.

In Run mode:

2.Key two initial estimates of the desired root, separated by v, into the X- and Y-registers. These estimates merely indicate to the calculator the approximate range of x in which it should initially seek a root of f(x) = 0.

3.Press ´ _ followed by the label of your subroutine. The calculator then searches for the desired zero of your function and displays the result. If the function that you are analyzing equals zero at more than one value of x, the routine will stop when it finds any one of those values. To find additional values, you can key in different initial estimates and use _again.

Immediately before _ addresses your subroutine it places a value of x in the X-, Y-, Z-, and T-registers. This value is then used by your subroutine to calculate f(x). Because the entire stack is filled with the x-value, this number is continually available to your subroutine. (The use of this technique is described on page 41).

Example: Use _to find the values of x for which

f(x) = x2 –3x– 10 = 0.

Using Horner's method (refer to page 79), you can rewrite f(x) so that it is programmed more efficiently:

f(x) = (x – 3)x – 10.

In Program mode, key in the following subroutine to evaluate f(x).

Keystrokes	Display
¥	000-	Program mode.
´ CLEAR M	000-	Clear program memory.