(11C) Quadratic Equation

[Gamo]

The program calculates the real or complex solutions of a quadratic equation.

aX^2 + bX + c = 0

c [ENTER] > b [ENTER] > a > [LBL A] briefly shown [+] or [-] solution.

If Positive (+) then two real solutions with R/S for second answer.
If Negative (-) then two complex solutions with X<>Y for complex of +,-

Program:

Code:


LBL A
LBL 1
ENTER
Rv
/
2
/
CHS
ENTER
X^2
Rv
Rv
X<>Y
/
STO 0
-
PSE
X<0
GTO 1
SQR
X<>Y
X<0
GTO 2
+
GTO 3
LBL 2
X<>Y
-
LBL 3
R/S
1/x
RCL 0
x
RTN
LBL 1
CHS
SQR
X<>Y
R/S

Example:
1) 2x^2 + 5x + 3 = 0

3 ENTER 5 ENTER 2 [A] > 0.0625 (Show briefly with positive) so the solutions are real:
Answer: -1.5 > [R/S] > -1
X={-1.5, -1}

2) 2x^2 + 3x + 4 = 0

4 ENTER 3 ENTER 2 [A] > -1.4375 (Show briefly with negative) so the solutions are complex:
Answer: -0.75 > [X<>Y] > 1.1990 round to 1.2
x1 = -0.75 + 1.2i
x2 = -0.75 - 1.2i

3) Here are examples of quadratic equations lacking the linear coefficient or the “bX”:

6x² + 144 = 0

144 ENTER 0 ENTER 6 [A] > -24 (Briefly show negative) solution are complex:
Answer: 0 > [X<>Y] > 4.8990
x1 = 4.8990i
x2 = -4.8990i

x² – 16 = 0

16 CHS ENTER 0 ENTER 1 [A] > (Briefly show positive) solution are real.
Answer: 4 > [R/S] > -4
x={4, -4}

4) Here are examples of quadratic equations lacking the constant term or “c”:

2x² + 8x = 0

0 ENTER 8 ENTER 2 [A] > (Briefly show positive) real solution.
Answer: -4 [R/S] > 0
x={0, -4}


Gamo