DuckieDai Quadratic Inequality Solver Python Program

Using the full toolkit? Read the step-by-step Polynomial Toolkit guide for quartic, cubic, and quadratic workflows, worked examples, and a reminder to keep every root you find.

algebra · MIT License

Overview

Solve a quadratic inequality using its real roots, leading sign, and endpoint inclusion.

Owner-tested on a TI calculator
Version 1.0.0
3796 bytes
Uses math

Download QINQS.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
The leading coefficient a is nonzero.
The program solves quadratics only; a zero leading coefficient is outside its supported input domain.
An a value of zero stops with a division-by-zero error because the quadratic formula divides by 2a.

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Source code

Download .py

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"""DuckieDai Quadratic Inequality 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 gcd(a,b):
    a=abs(a)
    b=abs(b)
    while b:
        a,b=b,a%b
    return a

def rat(n,d):
    if d<0:
        n=-n
        d=-d
    g=gcd(n,d)
    n//=g
    d//=g
    if d==1:
        return str(n)
    return str(n)+"/"+str(d)

def radroot(a,b,d,sgn):
    # simplify sqrt(d)
    k=1
    i=int(sqrt(d))
    while i>1:
        if d%(i*i)==0:
            k=i
            break
        i-=1

    r=d//(k*k)

    A=-b
    B=sgn*k
    C=2*a

    g=gcd(gcd(A,B),C)

    if g!=0:
        A//=g
        B//=g
        C//=g

    if C<0:
        A=-A
        B=-B
        C=-C

    if abs(B)==1:
        term="sqrt("+str(r)+")"
    else:
        term=str(abs(B))+"*sqrt("+str(r)+")"

    if A==0:
        if B<0:
            top="-"+term
        else:
            top=term
    else:
        if B<0:
            top=str(A)+"-"+term
        else:
            top=str(A)+"+"+term

    if C==1:
        return top

    return "("+top+")/"+str(C)


duckiedai_intro("Quad Inequality")

a=int(input("a: "))
b=int(input("b: "))
c=int(input("c: "))

print("1 >0")
print("2 >=0")
print("3 <0")
print("4 <=0")
op=input("Choice: ")

d=b*b-4*a*c

if d>0:

    q=int(sqrt(d))

    if q*q==d:
        n1=-b-q
        n2=-b+q
        den=2*a

        v1=n1/den
        v2=n2/den

        s1=rat(n1,den)
        s2=rat(n2,den)

    else:
        v1=(-b-sqrt(d))/(2*a)
        v2=(-b+sqrt(d))/(2*a)

        s1=radroot(a,b,d,-1)
        s2=radroot(a,b,d,1)

    if v1>v2:
        v1,v2=v2,v1
        s1,s2=s2,s1

    print("Roots:")
    print(s1)
    print(s2)
    print("Solution:")

    if a>0:
        if op=="1":
            print("(-inf,"+s1+")")
            print("U ("+s2+",inf)")
        elif op=="2":
            print("(-inf,"+s1+"]")
            print("U ["+s2+",inf)")
        elif op=="3":
            print("("+s1+","+s2+")")
        else:
            print("["+s1+","+s2+"]")

    else:
        if op=="1":
            print("("+s1+","+s2+")")
        elif op=="2":
            print("["+s1+","+s2+"]")
        elif op=="3":
            print("(-inf,"+s1+")")
            print("U ("+s2+",inf)")
        else:
            print("(-inf,"+s1+"]")
            print("U ["+s2+",inf)")

elif d==0:

    s=rat(-b,2*a)

    print("Root:",s)
    print("Solution:")

    if a>0:
        if op=="1":
            print("(-inf,"+s+")")
            print("U ("+s+",inf)")
        elif op=="2":
            print("ALL REAL")
        elif op=="3":
            print("EMPTY SET")
        else:
            print("{"+s+"}")
    else:
        if op=="1":
            print("EMPTY SET")
        elif op=="2":
            print("{"+s+"}")
        elif op=="3":
            print("(-inf,"+s+")")
            print("U ("+s+",inf)")
        else:
            print("ALL REAL")

else:

    print("No real roots")
    print("Solution:")

    if a>0:
        if op=="1" or op=="2":
            print("ALL REAL")
        else:
            print("EMPTY SET")
    else:
        if op=="3" or op=="4":
            print("ALL REAL")
        else:
            print("EMPTY SET")

"""DuckieDai Quadratic Inequality 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 gcd(a,b):
a=abs(a)
b=abs(b)
while b:
a,b=b,a%b
return a
def rat(n,d):
if d<0:
n=-n
d=-d
g=gcd(n,d)
n//=g
d//=g
if d==1:
return str(n)
return str(n)+"/"+str(d)
def radroot(a,b,d,sgn):
# simplify sqrt(d)
k=1
i=int(sqrt(d))
while i>1:
if d%(i*i)==0:
k=i
break
i-=1
r=d//(k*k)
A=-b
B=sgn*k
C=2*a
g=gcd(gcd(A,B),C)
if g!=0:
A//=g
B//=g
C//=g
if C<0:
A=-A
B=-B
C=-C
if abs(B)==1:
term="sqrt("+str(r)+")"
else:
term=str(abs(B))+"*sqrt("+str(r)+")"
if A==0:
if B<0:
top="-"+term
else:
top=term
else:
if B<0:
top=str(A)+"-"+term
else:
top=str(A)+"+"+term
if C==1:
return top
return "("+top+")/"+str(C)
duckiedai_intro("Quad Inequality")
a=int(input("a: "))
b=int(input("b: "))
c=int(input("c: "))
print("1 >0")
print("2 >=0")
print("3 <0")
print("4 <=0")
op=input("Choice: ")
d=b*b-4*a*c
if d>0:
q=int(sqrt(d))
if q*q==d:
n1=-b-q
n2=-b+q
den=2*a
v1=n1/den
v2=n2/den
s1=rat(n1,den)
s2=rat(n2,den)
else:
v1=(-b-sqrt(d))/(2*a)
v2=(-b+sqrt(d))/(2*a)
s1=radroot(a,b,d,-1)
s2=radroot(a,b,d,1)
if v1>v2:
v1,v2=v2,v1
s1,s2=s2,s1
print("Roots:")
print(s1)
print(s2)
print("Solution:")
if a>0:
if op=="1":
print("(-inf,"+s1+")")
print("U ("+s2+",inf)")
elif op=="2":
print("(-inf,"+s1+"]")
print("U ["+s2+",inf)")
elif op=="3":
print("("+s1+","+s2+")")
else:
print("["+s1+","+s2+"]")
else:
if op=="1":
print("("+s1+","+s2+")")
elif op=="2":
print("["+s1+","+s2+"]")
elif op=="3":
print("(-inf,"+s1+")")
print("U ("+s2+",inf)")
else:
print("(-inf,"+s1+"]")
print("U ["+s2+",inf)")
elif d==0:
s=rat(-b,2*a)
print("Root:",s)
print("Solution:")
if a>0:
if op=="1":
print("(-inf,"+s+")")
print("U ("+s+",inf)")
elif op=="2":
print("ALL REAL")
elif op=="3":
print("EMPTY SET")
else:
print("{"+s+"}")
else:
if op=="1":
print("EMPTY SET")
elif op=="2":
print("{"+s+"}")
elif op=="3":
print("(-inf,"+s+")")
print("U ("+s+",inf)")
else:
print("ALL REAL")
else:
print("No real roots")
print("Solution:")
if a>0:
if op=="1" or op=="2":
print("ALL REAL")
else:
print("EMPTY SET")
else:
if op=="3" or op=="4":
print("ALL REAL")
else:
print("EMPTY SET")

Filename: QINQS.py
Size: 3796 bytes
SHA-256: 90ff0c75184db4cc236faffc540e33191781c872370bbb558d78377f8051218b

Usage

Inputs

Integer coefficients a, b, and c for ax^2 + bx + c
One menu choice for strict or inclusive positive or negative results

Outputs

Roots in simplified rational or radical form
Interval, singleton, all-real, or empty-set solution

Units: Polynomial coefficients; no physical units.

Assumptions and limitations

Assumptions

The leading coefficient a is nonzero.

Constraints

The program solves quadratics only; a zero leading coefficient is outside its supported input domain.

Known failures

An a value of zero stops with a division-by-zero error because the quadratic formula divides by 2a.
A menu choice other than 1 to 4 is treated as choice 4.
Non-integer input uses the calculator Python input error path.

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 before the DuckieDai opening screen and website line were added. The steps after the opening screen are unchanged and were compared with the owner's file on desktop; this exact file has not yet been rerun on a calculator.
Dependencies: math
Suggested calculator name: QINQS — 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. QINQS 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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