The Museum of HP Calculators

Quadratic Equation: Real and Complex Solutions for the HP-33S

This program is by Eddie Shore and is used here by permission.

This program is supplied without representation or warranty of any kind. Eddie Shore and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.


This program solves the equation: Ax^2 + Bx + C = 0

x can be either real or complex solutions. This program uses one label (Q) and seven variables (A,B,C,D,E,F,G). Comments of entering the program will be noted on the program line.

To use: XEQ Q, enter A, R/S, enter B, R/S, enter C, R/S; the HP-33S displays the first root, note it (store if you wish), then press R/S for the second root. The root is complex if Flag 1 is set (flag 1 is a user flag).

Roots = -B/(2A) +- SQRT(B^2-4AC)/(2A)

I wrote this program on the HP 33S, but it should work with the 32S series as I understand the 33S is built on the 32S software.


Q0001  LBL Q             ' Set label Q
Q0002  INPUT A
Q0003  INPUT B
Q0004  INPUT C
Q0005  SQ(B)-4xAxC       ' Equation (enter by RS [right shift] EQN)
Q0006  STO D
Q0007  RCL D             ' Is the discriminant negative? 
Q0008  x<0?
Q0009  SF 1           ' Flag 1 - indicate that the roots are complex
Q0010  RCL D
Q0011  FS? 1
Q0012  +/-            ' The HP 33 can not take square roots of x<0
Q0013  square root
Q0014  STO E          '  E = abs(sqrt(D))
Q0015  -B/(2xA)       ' enter this as an equation
Q0016  STO F
Q0017  E/(2xA)        ' enter this an an equation
Q0018  STO G
Q0019  RCL G
Q0020  0              
Q0021  FS? 1
Q0022  x<>y
Q0023  RCL F
Q0024  0
Q0025  CMPLX+
Q0026  STOP           '  press the R/S key:  display first root
Q0027  RCL G
Q0028  +/-
Q0029  0
Q0030  RS? 1
Q0031  x<>y
Q0032  RCL F
Q0033  0
Q0034  CMPLX+
Q0035  STOP
Q0036  CF 1             ' clean up command
Q0037  RTN

Checksum = 7F5B;  Lines = 185

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