Threaded Mode | Linear Mode

Roberto Volpi · (This post was last modified: 05-20-2023 10:17 AM by Roberto Volpi.)

Hi all,

inspired by similar programs from classic HP models, here a short program to solve cubic equations in the form of Ax^3+Bx^2+Cx+D=0

The algorithm search the 1st root x1, always real, divides the polynomial by (x-x1) with synthetic division (Ruffini rule) to obtain a quadratic equation, and solve it to have 2nd and 3rd roots x2 and x3.

In case we have a quadratic equation in the form Ax^2+Bx+C=0 to solve, it processes directly to obtain the roots, real or complex.

LINE INSTRUCTION
C001 LBL C
C002 CLVARS
C003 STO D
C004 R down
C005 STO C
C006 R down
C007 STO B
C008 R down
C009 STO/B
C010 STO/C
C011 STO/D
C012 RCL D
C013 SGN
C014 STO H
C015 LAST X
C016 ABS
C017 RCL B
C018 ABS
C019 +
C020 10
C021 STO P
C022 R down
C023 1E-6
C024 STO O
C025 RCLxP
C026 X<=Y?
C027 GTO C025
C028 STO K
C029 RCL P
C030 STO/K
C031 RCL H
C032 +/-
C033 STO H
C034 RCL K
C035 RCLxH
C036 RCL+F
C037 STO G
C038 RCL F
C039 X=Y?
C040 GTO C059
C041 RCL G
C042 RCL+B
C043 RCLxG
C044 RCL+C
C045 RCLxG
C046 RCL+D
C047 STO L
C048 ABS
C049 RCL O
C050 X>Y?
C051 GTO C059
C052 RCL G
C053 STO F
C054 RCL L
C055 RCLxH
C056 X<0?
C057 GTO C034
C058 GTO C029
C059 RCL G
C060 R/S
C061 1
C062 X<>Y
C063 RCL+B
C064 ENTER
C065 RCLxG
C066 RCL+C
C067 GTO E001
E001 LBL E
E002 -2 i 0
E003 x
E004 LAST X
E005 R up
E006 x
E007 /
E008 X<>Y
E009 LAST X
E010 /
E011 ENTER
E012 ENTER
E013 x
E014 LAST X
E015 X<>Y
E016 R up
E017 -
E018 0.5
E019 Y^X
E020 -
E021 X<>Y
E022 LAST X
E023 +
E024 RTN

Instructions to solve cubic equation:

input A
press ENTER
input B
press ENTER
input C
press ENTER
input D
press XEQ C ENTER

the calculator shows first root x1, always real, in stack X, and the accuracy in stack Y

press R/S

the calculator shows 2nd and 3rd roots, x2 and x3, in stack Y and X.

The first real root x1 can be retrieved by pressing RCL G

Instructions to solve quadratic equations

input A
press ENTER
input B
press ENTER
input C
press XEQ E ENTER

the calculator shows both roots in stacks X and Y

Enjoy!