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(19C/29C) Solving second-degree equations
11-10-2023, 06:25 PM
Post: #1
(19C/29C) Solving second-degree equations
Here's just a little program for HP-19C/HP-29C which, starting from a second-degree equation, calculates exclusively in the stack :

- the discriminant Δ ;
- the successive X and Y coordinates of the extremum ;
- the real solution(s) if the discriminant is positive or zero;
- the real and imaginary solutions if the discriminant is negative.

To do this, enter the parameters a, b and c in Z, Y and X in the stack, then run the program using [GSB] [4].

For example, for the equation -x² + x + 1 = 0:
[1] [CHS] [ENTER] [CHS] [ENTER] [GSB] [4]; the calculator then displays Δ = 5, X=0.5, Y=1.25, x1≈1.618 and x2≈-0.618.

For the equation x² + 2x + 3 = 0:
[1] [ENTER] [2] [ENTER] [3] [GSB] [4]; then the calculator displays Δ = -8, X=-1, Y=2, the real part u=-1 and successively the two imaginary parts v1≈1.414 and v2≈-1.414.

[Image: 23111007070923397118298428.png]
[Image: 23111007070923397118298429.png]
[Image: 23111007072823397118298430.png]

Naturally, the program also works on the HP-29E calculator (where it was created).
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