Quadratic Formula

Description

Author: Eddie Shore, November 2011

This program find the roots the quadratic equation:

ax^2 + bx + c = 0

Instructions:
1. Store a in R0, b in R1, and c in R2.
2. Press [ f ] [ √ ] (A).
3. The discriminant is displayed (R0).
4. Press [R/S] displays R4.
5. Press [R/S] displays R5.

If R0 ≥ 0, R4 and R5 are the real roots of the quadratic equation.

If R0<0, R4 is the real part of the complex root, and R5 is ±imaginary part of the complex root.

Examples:

1. x^2 + 4x + 6
R1 = 1, R2 = 4, R3 = 6
Result: R0 = -8, R4 = -2, R5 ≈ 1.4142
The roots are -2 ± √2 i

2. x^2 - 5x + 3
R1 = 1, R2 = -5, R3 = 3
Result: R0 = 13, R5 ≈ 0.6972, R4 ≈ 4.3028
The roots are approximately 0.6972 and 4.3028.

STORAGE REGISTERS
0: Descriminant
1: a
2: b
3: c
4: Root 1/Real Part
5: Root 2/Imaginary Part

Program resources

Labels

Name Description
A Calculate Roots of the Quadratic Equation
0 Complex Roots Subroutine
1 -b/2a Subroutine

Storage Registers

Name Description
0 Discriminant; b^2 - 4 a c
1 a
2 b
3
4 Root 1/Real Part
5 Root 2/Imaginary Part

Program

Line Display Key Sequence Line Display Key Sequence
000 024 2 2
001 42.21.11 f LBL A 025 20
002 45 2 RCL 2 026 30
003 43 11 g 027 44 5 STO 5
004 4 4 028 43 32 g RTN
005 45.20. 1 RCL 1 029 42.21. 0 f LBL 0
006 45.20. 3 RCL 3 030 32 1 GSB 1
007 30 031 44 4 STO 4
008 44 0 STO 0 032 31 R/S
009 31 R/S 033 45 0 RCL 0
010 43.30. 2 g TEST x<0 034 43 16 g ABS
011 22 0 GTO 0 035 11 √x̅
012 4 4 036 2 2
013 10 ÷ 037 10 ÷
014 45 1 RCL 1 038 45.10. 1 RCL ÷ 1
015 43 11 g 039 44 5 STO 5
016 10 ÷ 040 43 32 g RTN
017 11 √x̅ 041 42.21. 1 f LBL 1
018 32 1 GSB 1 042 45 2 RCL 2
019 34 x↔y 043 16 CHS
020 40 044 2 2
021 44 4 STO 4 045 10 ÷
022 31 R/S 046 45.10. 1 RCL ÷ 1
023 43 36 g LSTx 047 43 32 g RTN