HP HP-15C

182 Section 13: Finding the Roots of an Equation
Keystrokes
Display
´ b 0
001–42,21, 0
Begin with b instruction.
Subroutine assumes stack
loaded with x.
3
002– 3
-
003– 30
Calculate x  3.
*
004– 20
Calculate (x  3)x.
1
005– 1
0
006– 0
-
007– 30
Calculate (x  3)x  10.
| n
008– 43 32
In Run mode, key two initial estimates into the X- and Y-registers.
Try estimates of 0 and 10 to look for a positive root.
Keystrokes
Display
*
| ¥
Run mode.
0 v
0.0000
Initial estimates.
10
10
You can now find the desired root by pressing ´_ 0. When you do
this, the calculator will not display the answer right away. The HP-15C uses
an iterative algorithm

to estimate the root. The algorithm analyzes your
function by sampling it many times, perhaps a dozen times or more. It does
this by repeatedly executing your subroutine. Finding a root will usually
require about 2 to 10 seconds; but sometimes the process will require even
more time.
Press ´_ 0 and sit back while your HP-15C exhibits one of its
powerful capabilities. The display flashes running while _ is
operating.
*
Press ´• 4 to obtain the displays shown here. The display setting does not influence the operation
of _.

An algorithm is a step-by-step procedure for solving a mathematical problem. An iterative algorithm is one
containing a portion that is executed a number of times in the process of solving the problem.