DuckieDai Cubic Zero Solver Python Program

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algebra · MIT License

Overview

Test one supplied zero of a cubic, then solve the resulting quadratic quotient when that zero is confirmed.

Owner-tested on a TI calculator
Version 1.0.0
3934 bytes
Uses math

Download synthD.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer to the Python App; the owner's transfer details were not recorded
Inputs represent a non-degenerate cubic and a valid numeric or p/q zero.
The solver only continues after the supplied candidate is confirmed as a zero.
Remainders with magnitude below 1e-7 are treated as zero.

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Source code

Download .py

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"""DuckieDai Cubic Zero Solver for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("| hiddenwordscanner.com|")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 8)


def clear_screen():
    print("\n" * 8)


def clean_num(n):
    if abs(n - round(n)) < 0.0000001:
        return int(round(n))
    return round(n, 6)


def quadratic_solver(a, b, c):
    disc = b * b - 4 * a * c

    # SCREEN 3
    clear_screen()

    print("QUADRATIC")
    print("---------")
    print(clean_num(a), "x^2")
    print(clean_num(b), "x")
    print(clean_num(c))

    print("")
    print("Discriminant:")
    print(clean_num(disc))

    input("\nPress enter ")

    # SCREEN 4
    clear_screen()

    print("OTHER ROOTS")
    print("-----------")

    if abs(disc) < 0.0000001:
        x = -b / (2 * a)

        print("One repeated root:")
        print(clean_num(x))

    elif disc > 0:
        x1 = (-b + sqrt(disc)) / (2 * a)
        x2 = (-b - sqrt(disc)) / (2 * a)

        print("x1 =", clean_num(x1))
        print("x2 =", clean_num(x2))

        print("")
        print("Exact form:")
        print(clean_num(-b), "+/-")
        print("sqrt(", clean_num(disc), ")")
        print("over", clean_num(2 * a))

    else:
        real = -b / (2 * a)
        imag = sqrt(-disc) / abs(2 * a)

        print("Complex roots:")
        print(clean_num(real), "+")
        print(clean_num(imag), "i")
        print("")
        print(clean_num(real), "-")
        print(clean_num(imag), "i")

    input("\nPress enter ")


def number(prompt):
    text = input(prompt)

    if "/" in text:
        parts = text.split("/")
        return float(parts[0]) / float(parts[1])

    return float(text)


def run_test():
    clear_screen()

    print("ENTER CUBIC")
    print("ax^3+bx^2+cx+d")
    print("")

    a = float(input("x^3: "))
    b = float(input("x^2: "))
    c = float(input("x: "))
    d = float(input("Const: "))

    print("")
    print("Test zero")
    print("Use decimal if frac")
    zero = number("Zero: ")

    first = a
    second = b + first * zero
    third = c + second * zero
    remainder = d + third * zero

    # Fix tiny floating errors
    if abs(remainder) < 0.0000001:
        remainder = 0

    # SCREEN 1
    clear_screen()

    print("ZERO TEST")
    print("---------")
    print("Test:", clean_num(zero))
    print("R:", clean_num(remainder))
    print("")

    if remainder == 0:
        print("TRUE!")
        print("IT IS A ZERO")
    else:
        print("FALSE")
        print("NOT A ZERO")

    input("\nPress enter ")

    # If false, stop here
    if remainder != 0:
        return

    # SCREEN 2
    clear_screen()

    print("QUOTIENT")
    print("--------")
    print(clean_num(first), "x^2")
    print(clean_num(second), "x")
    print(clean_num(third))

    print("")
    print("Next:")
    print("Quadratic formula")

    input("\nPress enter ")

    # AUTOMATICALLY SOLVE QUADRATIC
    quadratic_solver(first, second, third)

    # FINAL SCREEN
    clear_screen()

    print("ALL ROOTS")
    print("---------")
    print("First root:")
    print(clean_num(zero))
    print("")
    print("Other 2 shown")
    print("on last screen")


duckiedai_intro("Cubic Solver")

while True:
    run_test()

    print("")
    again = input("Again? y/n: ")

    if again.lower() != "y":
        break


clear_screen()
print("DuckieDai says: done!")

"""DuckieDai Cubic Zero Solver for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("| hiddenwordscanner.com|")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 8)
def clear_screen():
print("\n" * 8)
def clean_num(n):
if abs(n - round(n)) < 0.0000001:
return int(round(n))
return round(n, 6)
def quadratic_solver(a, b, c):
disc = b * b - 4 * a * c
# SCREEN 3
clear_screen()
print("QUADRATIC")
print("---------")
print(clean_num(a), "x^2")
print(clean_num(b), "x")
print(clean_num(c))
print("")
print("Discriminant:")
print(clean_num(disc))
input("\nPress enter ")
# SCREEN 4
clear_screen()
print("OTHER ROOTS")
print("-----------")
if abs(disc) < 0.0000001:
x = -b / (2 * a)
print("One repeated root:")
print(clean_num(x))
elif disc > 0:
x1 = (-b + sqrt(disc)) / (2 * a)
x2 = (-b - sqrt(disc)) / (2 * a)
print("x1 =", clean_num(x1))
print("x2 =", clean_num(x2))
print("")
print("Exact form:")
print(clean_num(-b), "+/-")
print("sqrt(", clean_num(disc), ")")
print("over", clean_num(2 * a))
else:
real = -b / (2 * a)
imag = sqrt(-disc) / abs(2 * a)
print("Complex roots:")
print(clean_num(real), "+")
print(clean_num(imag), "i")
print("")
print(clean_num(real), "-")
print(clean_num(imag), "i")
input("\nPress enter ")
def number(prompt):
text = input(prompt)
if "/" in text:
parts = text.split("/")
return float(parts[0]) / float(parts[1])
return float(text)
def run_test():
clear_screen()
print("ENTER CUBIC")
print("ax^3+bx^2+cx+d")
print("")
a = float(input("x^3: "))
b = float(input("x^2: "))
c = float(input("x: "))
d = float(input("Const: "))
print("")
print("Test zero")
print("Use decimal if frac")
zero = number("Zero: ")
first = a
second = b + first * zero
third = c + second * zero
remainder = d + third * zero
# Fix tiny floating errors
if abs(remainder) < 0.0000001:
remainder = 0
# SCREEN 1
clear_screen()
print("ZERO TEST")
print("---------")
print("Test:", clean_num(zero))
print("R:", clean_num(remainder))
print("")
if remainder == 0:
print("TRUE!")
print("IT IS A ZERO")
else:
print("FALSE")
print("NOT A ZERO")
input("\nPress enter ")
# If false, stop here
if remainder != 0:
return
# SCREEN 2
clear_screen()
print("QUOTIENT")
print("--------")
print(clean_num(first), "x^2")
print(clean_num(second), "x")
print(clean_num(third))
print("")
print("Next:")
print("Quadratic formula")
input("\nPress enter ")
# AUTOMATICALLY SOLVE QUADRATIC
quadratic_solver(first, second, third)
# FINAL SCREEN
clear_screen()
print("ALL ROOTS")
print("---------")
print("First root:")
print(clean_num(zero))
print("")
print("Other 2 shown")
print("on last screen")
duckiedai_intro("Cubic Solver")
while True:
run_test()
print("")
again = input("Again? y/n: ")
if again.lower() != "y":
break
clear_screen()
print("DuckieDai says: done!")

Filename: synthD.py
Size: 3934 bytes
SHA-256: f4c36ab4cc6940021758957bcd5cb9c3e2beefa62bd56aac0fa11b74e9eb73c6

Usage

Inputs

Numeric coefficients a, b, c, and d for ax^3 + bx^2 + cx + d
One decimal or p/q-form proposed zero

Outputs

True or false zero result
Quadratic quotient
Remaining real, repeated, or complex roots when the tested zero is true

Units: Polynomial coefficients; no physical units.

Assumptions and limitations

Assumptions

Inputs represent a non-degenerate cubic and a valid numeric or p/q zero.

Constraints

The solver only continues after the supplied candidate is confirmed as a zero.
Remainders with magnitude below 1e-7 are treated as zero.

Known failures

Malformed fractions and zero denominators use the calculator Python input error path.
A zero leading coefficient can create invalid quadratic-formula arithmetic.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally testing this program on a TI-84 Plus CE Python calculator; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator. The published file is the owner's tested source.
Dependencies: math
Suggested calculator name: SYNTHD — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Confirm that your calculator is the Python-capable model named above. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. SYNTHD is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

Availability does not mean a teacher, school, or exam permits this program. Follow the applicable rules.

Version history

1.0.0 — current version, published 2026-10-03. Download this reviewed version

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