HP 32SII Mathematics Programs 15–21

Uses order to select root finding routine.

Program Listing: Program Lines:   

b0 = a0(4a2 – a32) – a12.

Let y0 be the largest real root of the above cubic. Then the fourth–order polynomial is reduced to two quadratic polynomials:

			x2 + (J + L)⋅ + (K + M) = 0
			x2 + (J – L)x + (K – M) = 0
where J = a3/2
K = y0 /2
L =	J2 − a + y	0	⋅ (the sign of JK – a1/2)
	2
M =	K2 − a2

Roots of the fourth degree polynomial are found by solving these two quadratic polynomials.

A quadratic equation x2 + a1x + a0 = 0 is solved by the formula

x	= − a1 ±	(a1)2 − a
1,2	2	2	0

If the discriminant d = (a1/2)2 – ao ≥ 0, the roots are real; if d < 0, the roots are complex, being u ± iv = −(a1 2) ± i − d .

Description

Defines the beginning of the polynomial root finder routine.

 "! Prompts for and stores the order of the polynomial.  ! L Uses order as loop counter.

Checksum and length: 699F 004.5

   Starts prompting routine.  "!1L2Prompts for a coefficient.    L Counts down the input loop.  !  Repeats until done.

    ! L

Mathematics Programs 15–21

File name 32sii-Manual-E-0424
Printed Date : 2003/4/24	Size : 17.7 x 25.2 cm