HP 15C Manual do Utilizador descarregar pdf (Página 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)

= 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)

Example: Use deflation to help find the roots of

60x

 944x

+ 3003x

+ 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-

´b2

001-42,21, 2

002– 6

003– 0

004– 20

005– 9

006– 4

007– 4

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HP 15C Manual do Utilizador Página 234