HP HP-15C - Page 234

234 Appendix D: A Detailed Look at _
add a few program lines at the end of your function subroutine. These lines
should subtract the known root (to 10 significant digits) from the x-value
and divide this difference into the function value. In many cases the root
will be a simple one, and the new function will direct _ away from
the known root. On the other hand, the root may be a multiple root. A
multiple root is one that appears to be present repeatedly, in the following
sense: at such a root, not only does the graph of f(x) cross the x-axis, but its
slope (and perhaps the next few higher-order derivatives) also equals zero.
If the known root of your equation is a multiple root, the root is not
eliminated by merely dividing by the factor described above. For example,
the equation
f(x) = x(x – a)
3
= 0
has a multiple root at x = a (with a multiplicity of 3). This root is not
eliminated by dividing f(x) by (x  a). But it can be eliminated by dividing
by (x  a)
3
.
Example: Use deflation to help find the roots of
60x
4
 944x
3
+ 3003x
2
+ 6171x – 2890 = 0.
Using Horner's method, this equation can be rewritten in the form
(((60x  944)x + 3003)x + 6171)x  2890 = 0.
Program a subroutine that evaluates the polynomial.
Keystrokes
Display
|¥
000-
Program mode.
´ CLEAR
M
000-
´b2
001-42,21, 2
6
002– 6
0
003– 0
*
004– 20
9
005– 9
4
006– 4
4
007– 4