HP 15c Scientific 002–, 003–, 004–, 005–, 006–, 007–, 001-42,21,2

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

60x4 – 944x3 + 3003x2 + 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	000-
M
´b2	001-42,21, 2
6	002–	6
0	003–	0
*	004–	20
9	005–	9
4	006–	4
4	007–	4