(17BII and 27S) Quadratic Equation

[Eddie W. Shore]

The following solver equations solve the quadratic equation

A*x^2 + B*x + C = 0

by the famous Quadratic Formula

x = (-B ± √(B^2 - 4*A*C) ) / (2*A)

Define D as the discriminant: D = B^2 - 4*A*C

If A, B, and C are real numbers and:

D<0, the roots are complex conjugates

D≥0, the roots are real roots

Quadratic Equation: Real Roots Only

Code:

QUAD:X=INV(2*A)*(-B+SQRT(B^2-4*A*C)*SGN(R#))

Input Variables:
A: coefficient of X^2
B: coefficient of X
C: constant
R#: -1 or 1

Output Varibles:
X: root

Example: 2X^2 + 3X - 5 = 0

Input:
A: 2
B: 3
C: -5
R#: 1 (or any positive number)

Output:
X = 1

Input:
R#: -1

Output:
X = -2.5

Quadratic Equation: Real or Complex Roots
(Let (L) and Get (G) functions required)

Code:

QUAD:0*(A+B+C+L(D:B^2-4*A*C)+L(E:2*A))
+IF(S(X1):IF(D<0:-B÷G(E):(-B+SQRT(D))÷G(E))-X1:0)
+IF(S(X2):IF(D<0:SQRT(ABS(D))÷G(E):(-B-SQRT(D))÷G(E))-X2:0)

Input Variables:
A: coefficient of X^2
B: coefficient of X
C: constant

Output Variables:
D: Discriminant
If D<0: X1: real part, X2: imaginary part
If D≥0: X1: real root 1, X2: real root 2

Example 1: -3*X^2 + 8*X - 1= 0

Input:
A: -3
B: 8
C: -1

Output:
D = 52
X1 = 0.1315
X2 = 2.5352

Roots: x = 0.1315, x = 2.5352

Example 2: 3*X^2 + 5*X + 3 = 0

Input:
A: 3
B: 5
C: 3

Output:
D = -11
X1 = -0.8333
X2 = 0.5528

Roots: x = -0.8333 ± 0.5528i

Link: https://edspi31415.blogspot.com/2019/03/...rmula.html