HP 33s - Manual (Page 242)

15–20 Mathematics Programs
g
@
.
)
 Displays next value.
g
@
)
  Displays next value.
g
@
)
  Displays next value.
X I
)
 Inverts inverse to produce original
matrix.
X A @
)
 Begins review of inverted matrix.
g
@
)
 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
x
n
+ a
n–1
x
n–1
+ ... + a
1
x + a
0
= 0
where n = 2, 3, 4, or 5. The coefficient of the highest–order term (a
n
) 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:
y
3
+ b
2
y
2
+ b
1
y + b
0
= 0
where b
2
= – a
2
b
1
= a
3
a
1
– 4a
0