(11C) CUBIC EQUATION
06-09-2018, 06:05 PM (This post was last modified: 06-09-2018 07:14 PM by Dieter.)
Post: #6
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: (11C) CUBIC EQUATION
(06-09-2018 12:54 PM)Dieter Wrote:  Maybe I can post a program that calculates the solutions directly. This should be much faster.

OK, here it is. This should run on various classic RPN HPs, including the 11C, 15C, 67/97, 41 and maybe others.

Code:
001  LBL C 002  STO 3 003  R↓ 004  STO 2 005  R↓ 006  STO 1 007  R↓ 008  STO/1 009  STO/2 010  STO/3 011  RCL 1 012  ENTER 013  x^2 014  4 015  . 016  5 017  / 018  RCL 2 019  - 020  RCL 1 021  3 022  / 023  STO 1 024  * 025  STO+3 026  R↓ 027  RCL 1 028  * 029  STO-2 030  RCL 2 031  3 032  / 033  ENTER 034  X^2 035  * 036  STO 0 037  RCL 3 038  2 039  / 040  x^2 041  + 042  x<0? 043  GTO 3 044  SQRT 045  ENTER 046  ENTER 047  RCL 3 048  2 049  / 050  - 051  X<>Y 052  LastX 053  + 054  CHS 055  GSB 0 056  STO 2 057  STO 3 058  X<>Y 059  GSB 0 060  STO+2 061  STO-3 062  LBL 2 063  RCL 2 064  RCL 1 065  - 066  R/S 067  RCL 2 068  2 069  / 070  RCL 1 071  + 072  CHS 073  RCL 3 074  . 075  7 076  5 077  SQRT 078  * 079  ABS 080  PAUSE 081  X<>Y 082  R/S 083  GTO 2 084  LBL 0 085  x=0? 086  RTN 087  ENTER 088  ABS 089  / 090  LastX 091  3 092  1/x 093  Y^X 094  * 095  RTN 096  LBL 3 097  RCL 3 098  CHS 099  2 100  / 101  RCL 0 102  CHS 103  SQRT 104  / 105  COS-1 106  3 107  STO/2 108  / 109  STO 3 110  RCL 2 111  CHS 112  SQRT 113  2 114  * 115  STO 2 116  LBL 1 117  RCL 2 118  RCL 3 119  COS 120  * 121  RCL 1 122  - 123  R/S 124  ENTER 125  . 126  5 127  CHS 128  COS-1 129  STO-3 130  GTO 1

The program determines the roots for ax³+bx²+cx+d.
It uses the data registers 0...3. "COS-1" is the inverse cosine (cos–1).
If you want to see the discriminant you may insert a PAUSE between line 041 and 042.
Even on slow machines like the 11C or 67/97 the program should run within a few seconds.

Usage:
a [ENTER] b [ENTER] c [ENTER] d

[C] => first real root

- if three real roots exist:
[R/S] => second root
[R/S] => third root

- if the other two roots are complex (conjugate):
[R/S] => "imaginary part", real part
Both parts can be reviewed with the [X<>Y] key.

Examples:

2x³ + 3x² – 6x – 5

2 [ENTER] 3 [ENTER] 6 [CHS] [ENTER] 5 [CHS]
[C]    1,5297
[R/S] –0,7022
[R/S] –2,3275

x³ + x² + x – 1

1 [ENTER] 1 [ENTER] 1 [ENTER] 1 [CHS]
[C]    0,5437
[R/S] "1,1151"  –0,7718

So the real root is at 0,5437 and the two others are –0,7718 ±1,1151 i.

Dieter
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 Messages In This Thread (11C) CUBIC EQUATION - Gamo - 06-09-2018, 11:49 AM RE: (11C) CUBIC EQUATION - Gamo - 06-09-2018, 12:34 PM RE: (11C) CUBIC EQUATION - Dieter - 06-09-2018, 12:54 PM RE: (11C) CUBIC EQUATION - rprosperi - 06-09-2018, 01:00 PM RE: (11C) CUBIC EQUATION - Massimo Gnerucci - 06-09-2018, 01:18 PM RE: (11C) CUBIC EQUATION - Dieter - 06-09-2018 06:05 PM RE: (11C) CUBIC EQUATION - Dieter - 06-09-2018, 07:50 PM RE: (11C) CUBIC EQUATION - Valentin Albillo - 06-09-2018, 10:34 PM RE: (11C) CUBIC EQUATION - Dieter - 06-10-2018, 07:15 AM RE: (11C) CUBIC EQUATION - Valentin Albillo - 06-10-2018, 08:50 PM RE: (11C) CUBIC EQUATION - Dieter - 06-10-2018, 09:17 PM RE: (11C) CUBIC EQUATION - Albert Chan - 07-20-2021, 10:12 PM RE: (11C) CUBIC EQUATION - Gamo - 06-10-2018, 02:42 AM RE: (11C) CUBIC EQUATION - Gamo - 06-10-2018, 02:36 PM RE: (11C) CUBIC EQUATION - Dieter - 06-10-2018, 03:34 PM RE: (11C) CUBIC EQUATION - Dieter - 06-10-2018, 09:35 PM RE: (11C) CUBIC EQUATION - Gamo - 06-11-2018, 02:16 AM RE: (11C) CUBIC EQUATION - Dieter - 06-11-2018, 07:04 AM RE: (11C) CUBIC EQUATION - Gamo - 06-11-2018, 08:19 AM RE: (11C) CUBIC EQUATION - Dieter - 06-11-2018, 08:19 PM RE: (11C) CUBIC EQUATION - Gamo - 06-12-2018, 07:02 AM

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