HP 32SII - Manual (Page 247)

Mathematics Programs 15–21
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
b
0
= a
0
(4a
2
– a
32
) – a
12
.
Let y
0
be the largest real root of the above cubic. Then the fourth–order
polynomial is reduced to two quadratic polynomials:
x 2 + (J + L) × + (K + M) = 0
x 2 + (J – L)x + (K – M) = 0
where J = a
3
/2
K = y
0
/2
L =
0 2
2 y a J + − × (the sign of JK – a
1
/2)
M =
2
2 a K −
Roots of the fourth degree polynomial are found by solving these two
quadratic polynomials.
A quadratic equation x 2 + a
1
x + a
0
= 0 is solved by the formula
0
2 1 1
2 , 1
)
2
(
2
a
a a
x − ± − =
If the discriminant d = (a
1
/2) 2 – a
o
≥ 0, the roots are real; if d < 0, the roots
are complex, being d i a iv u − ± − = ± ) 2 (
1
.
Program Listing:
Program Lines: 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.
"!1L2 Prompts for a coefficient.
L Counts down the input loop.
! Repeats until done.
! L Uses order to select root finding routine.