HP 33s Scientific manual Terms and Coefficients, Order

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 XP 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	x5	x4	x3	x2	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 grepeatedly 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.

Mathematics Programs 15–29