HP 15C: Quadratic Solver Using Solve and Flags
Introduction
This program solves the quadratic equation for real roots:
a x^2 + b x + c = 0
Instructions:
1. Key: a [ENTER], b [ENTER], c [ f ] [ A ] (enter coefficients into label A)
2. The first root is displayed.
3. Press [ R/S ] for the second root.
Registers Used:
R1 = a
R2 = b
R3 = c
R4 = root 1
R5 = root 2
R6 = abs((R1 + R2 + R3) ÷ 3), I use [-R6, R6] as my initial guesses.
Flag 0: used to adjust the equation to be solved
Equation 1: finding the first root: (a x^2 + b x + c) (flag 0 is set)
Equation 2: finding the first root: (a x^2 + b x + c) ÷ (x - root) (flag 0 is clear, this is a depressed equation)
When a function with multiple roots is present, we can take out roots already found by dividing f(x) by (x - root).
HP 15C Program: Quadratic Solver
Steps: 47, Bytes: 57
Code:
Step : Key Code : Key
001 : 42,21,11 : LBL A
002 : 44, 3 : STO 3
003 : 44, 6 : STO 6
004 : 33 : R↓
005 : 44, 2 : STO 2
006 : 44,40, 6 : STO+ 6
007 : 33 : R↓
008 : 44, 1 : STO 1
009 : 44,40, 6 : STO+ 6
010 : 45, 6 : RCL 6
011 : 3 : 3
012 : 10 : ÷
013 : 43,16 : ABS
014 : 44, 6 : STO 6
015 : 43, 4, 0 : SF 0
016 : 42,21, 0 : LBL 0
017 : 45, 6 : RCL 6
018 : 16 : CHS
019 : 45, 6 : RCL 6
020 : 42,10, 1 : SOLVE 1
021 : 43, 6, 0 : F? 0
022 : 22, 2 : GTO 2
023 : 22, 3 : GTO 3
024 : 42,21, 2 : LBL 2
025 : 44, 4 : STO 4
026 : 43, 5, 0 : CF 0
027 : 22, 0 : GTO 0
028 : 42,21, 1 : LBL 1
029 : 36 : ENTER
030 : 36 : ENTER
031 : 45,20, 1 : RCL× 1
032 : 45,40, 2 : RCL+ 2
033 : 20 : ×
034 : 45,40, 3 : RCL+ 3
035 : 43, 6, 0 : F? 0
036 : 43, 32 : RTN
037 : 34 : x<>y
038 : 45, 4 : RCL 4
039 : 30 : -
040 : 10 : ÷
041 : 43,32 : RTN
042 : 42,21, 3 : LBL 3
043 : 44, 5 : STO 5
044 : 45, 4 : RCL 4
045 : 31 : R/S
046 : 34 : x<>y
047 : 43, 32 : RTN
Examples
x^2 - 5 x - 24 = 0
a = 1
b = -5
c = -24
1 [ ENTER ] 5 [CHS] [ ENTER ] 24 [ CHS ] [ f ] [ A ]
Roots: 8 [ R/S ] -3 (x = 8, x= -3)
2 x^2 + 8 x - 2 = 0
a = 2
b = 8
c = -2
2 [ ENTER ] 8 [ ENTER ] 2 [ CHS ] [ f ] [ A ]
Roots: 0.2361 [ R/S ] -4.2361 (x ≈ 0.2361, x ≈ -4.2361)
Eddie
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