Hp 33s User Manual download pdf (Page 242)

100

101

15–20 Mathematics Programs

@

.)

Displays next value.

@

)

Displays next value.

@

)

Displays next value.

)

Inverts inverse to produce ori

inal

matrix.

@

)

Begins review of inverted matrix.

@

)

Displays next value, ...... and so

on.

Polynomial Root Finder

This program finds the roots of a polynomial of order 2 through 5 with real

coefficients. It calculates both real and complex roots.

For this program, a general polynomial has the form

+ a

n–1

+ ... + a

x + a

= 0

where n = 2, 3, 4, or 5. The coefficient of the highest–order term (

) is assumed to

be 1. If the leading coefficient is not 1, you should make it 1 by dividing all the

coefficients in the equation by the leading coefficient. (See example 2.)

The routines for third– and fifth–order polynomials use SOLVE to find one real root

of the equation, since every odd–order polynomial must have at least one real root.

After one root is found, synthetic division is performed to reduce the original

polynomial to a second– or fourth–order polynomial.

To solve a fourth–order polynomial, it is first necessary to solve the resolvant cubic

polynomial:

+ b

y + b

= 0

where

= – a

= a

– 4a

1 2 ... 237 238 239 240 241 242 243 244 245 246 247 ... 386 387

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Hp 33s User Manual Page 242

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