Quadratic Equation Solver program for the HP-15C

Description

This program finds the roots of a quadratic equation of the form ax2 + bx + c = 0.

Push a, b, and c into the Z, Y, and X registers of the stack respectively, then press the E function key. The roots of the equation will appear in the X and Y registers.

If the "C" indicator appears then one or more of the roots are complex numbers.

Program resources

Labels

Name Description
E Compute the Roots of the Quadratic Equation
18 Used for internal computation
19 Used for internal computation

Storage Registers

Name Description
0 Used for internal computation
1 Used for internal computation
2 Used for internal computation
3 Used for internal computation
10 Used for internal computation
11 Used for internal computation
12 Used for internal computation
13 Used for internal computation

Flags

Number Description
8 Set to indicate that the result is a complex number

Program

Line Display Key Sequence Line Display Key Sequence Line Display Key Sequence
000    032 45.10. 1   RCL ÷ 1 064 45 ;3   RCL . 3
001 42.21.15 f LBL E 033 44 ;0   STO . 0 065 42 25   f I
002 43. 6. 8   g F? 8 034 45 2   RCL 2 066 20   ✕
003 22 ;9   GTO . 9 035 45.10. 1   RCL ÷ 1 067 2   2
004 44 3   STO 3 036 42 25   f I 068 20   ✕
005 33   R⬇ 037 42 30   f Re↔Im 069 30   −
006 16   CHS 038 45 2   RCL 2 070 42 31   f PSE
007 44 2   STO 2 039 45.10. 1   RCL ÷ 1 071 42 30   f Re↔Im
008 43 11   g x² 040 45 ;0   RCL . 0 072 42 31   f PSE
009 34   x↔y 041 16   CHS 073 42 30   f Re↔Im
010 2   2 042 42 25   f I 074 11   √x̅
011 20   ✕ 043 43 32 g RTN 075 44 0   STO 0
012 44 1   STO 1 044 42.21. ;9 f LBL . 9 076 42 30   f Re↔Im
013 45.20. 3   RCL ✕ 3 045 44 3   STO 3 077 44 ;0   STO . 0
014 2   2 046 42 30   f Re↔Im 078 45.40. ;2   RCL ✛ . 2
015 20   ✕ 047 44 ;3   STO . 3 079 42 30   f Re↔Im
016 30   − 048 33   R⬇ 080 45.40. 2   RCL ✛ 2
017 42 31   f PSE 049 16   CHS 081 45 1   RCL 1
018 43.30. 2   g TEST x<0 050 44 2   STO 2 082 45 ;1   RCL . 1
019 22 ;8   GTO . 8 051 42 30   f Re↔Im 083 42 25   f I
020 11   √x̅ 052 16   CHS 084 10   ÷
021 44 0   STO 0 053 44 ;2   STO . 2 085 45 2   RCL 2
022 45.40. 2   RCL ✛ 2 054 42 30   f Re↔Im 086 45.30. 0   RCL − 0
023 45.10. 1   RCL ÷ 1 055 11   √x̅ 087 45 ;2   RCL . 2
024 45 2   RCL 2 056 34   x↔y 088 45.30. ;0   RCL − . 0
025 45.30. 0   RCL − 0 057 2   2 089 42 25   f I
026 45.10. 1   RCL ÷ 1 058 20   ✕ 090 45 1   RCL 1
027 43 32 g RTN 059 44 1   STO 1 091 45 ;1   RCL . 1
028 42.21. ;8 f LBL . 8 060 42 30   f Re↔Im 092 42 25   f I
029 43. 4. 8   g SF 8 061 44 ;1   STO . 1 093 10   ÷
030 11   √x̅ 062 42 30   f Re↔Im 094 43 32 g RTN
031 42 30   f Re↔Im 063 45 3   RCL 3