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HP 17BII and HP 27S: Quadratic Formula

HP 17BII and HP 27S:  Quadratic Formula

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
D≥0, the roots are real roots

Quadratic Equation:  Real Roots Only

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)

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

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

Output Variables:
D:  Discriminant
If DIf 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

Eddie

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