HP 33s - Manual (Page 251)

Mathematics Programs 15–29
Because of round–off error in numerical computations, the program may produce
values that are not true roots of the polynomial. The only way to confirm the roots is
to evaluate the polynomial manually to see if it is zero at the roots.
For a third– or higher–order polynomial, if SOLVE cannot find a real root, the error
# &
is displayed.
You can save time and memory by omitting routines you don't need. If you're not
solving fifth–order polynomials, you can omit routine E. If you're not solving fourth–
or fifth–order polynomials, you can omit routines D, E, and F. If you're not solving
third–, fourth–, or fifth–order polynomials, you can omit routines C, D, E, and F.
Program Instructions:
1. Press { c {} to clear all programs and variables.
2. Key in the program routines; press ‡ when done.
3. Press X P to start the polynomial root finder.
4. Key in F, the order of the polynomial, and press g
5. At each prompt, key in the coefficient and press g . You're not prompted for
the highest–order coefficient — it's assumed to be 1. You must enter 0 for
coefficients that are 0. Coefficient A must not be 0.
Terms and Coefficients
Order x
5
x
4
x
3
x
2
x Constant
5 1 E D C B A
4 1 D C B A
3 1 C B A
2 1 B A
6. After you enter the coefficients, the first root is calculated. A real root is
displayed as %/real value. A complex root is displayed as %/ real part,
(Complex roots always occur in pairs of the form u ± i v, and are labeled in the
output as %/real part and i =imaginary part, which you'll see in the next step.)
7. Press g repeatedly to see the other roots, or to see i = imaginary part, the
imaginary part of a complex root. The order of the polynomial is same as the
number of roots you get.
8. For a new polynomial, go to step 3.