QuadCalculator

A quadratic equation solver written in modern C++. It supports both real and complex coefficients and computes roots using the quadratic formula.

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📖 The Quadratic Equation

A quadratic equation is of the form:

$$ax^2 + bx + c = 0, \quad a \neq 0$$

The discriminant is given by:

$$\Delta = b^2 - 4ac$$

The roots are then:

$$x_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2a}$$

Root Types

• If $\Delta > 0$: two distinct real roots.
• If $\Delta = 0$: one real repeated root.
• If $\Delta < 0$: two complex conjugate roots.

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🚀 Features

• Compute real roots and complex roots of any quadratic equation.
• Accept coefficients in both real and complex form.
• Support for square root notation in input (e.g. sqrt(3), 2sqrt(5), -sqrt(7)).
• Colored console output for clarity (on supported terminals).
• Cross-platform compatibility (Linux, macOS, Windows).

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🔧 Build Instructions

Requirements

• A C++20 compiler (GCC ≥ 10, Clang ≥ 10, MSVC ≥ 2019)
• CMake ≥ 3.16

Steps

git clone https://github.com/yourname/QuadCalculator.git
cd QuadCalculator
mkdir build && cd build
cmake ..
cmake --build .

This will produce an executable named QuadCalc (or QuadCalc.exe on Windows).

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🖥️ Usage

Display Help

./QuadCalc -h

Solve with Real Coefficients

Mode: -r

./QuadCalc -r 1 -3 2

Output:

The discriminant is: 1
Root 1 : (2.00)
Root 2 : (1.00)

Supports square root notation:

./QuadCalc -r 1 sqrt(2) 3

Solve with Complex Coefficients

Mode: -cc

Arguments are written as real,imag. Example:

./QuadCalc -cc 1,2 3,4 5,6

Output:

The discriminant is: (-28.00 + 44.00i)
Root 1 : (-0.23 + 0.69i)
Root 2 : (-2.77 - 1.69i)

You can also use square root syntax inside components:

./QuadCalc -cc "2,sqrt(3)" "3,4" "5,6"

⚠️ Note for zsh/fish users: Quote arguments containing parentheses, e.g. "sqrt(3)".

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📂 Input Syntax

Real Coefficients (-r)

• Numbers: 1, -3, 2.5
• Square roots: sqrt(3), 2sqrt(5), -sqrt(7)

Complex Coefficients (-cc)

• Format: real,imag
• Examples:
  • 1,2 → $1 + 2i$
  • -3,0 → $-3$
  • 0,-4 → $-4i$
• Both real and imaginary parts support sqrt(...).
• Shell-friendly form (alternative):

./QuadCalc -cc 1 2 3 4 5 6   # treated as (1+2i), (3+4i), (5+6i)

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📘 Examples

Example 1 — Real Roots

./QuadCalc -r 1 -5 6

Equation: $x^2 - 5x + 6 = 0$
Discriminant: $\Delta = 25 - 24 = 1$
Roots: $x_1 = 3, x_2 = 2$

Example 2 — Complex Roots

./QuadCalc -r 1 2 5

Equation: $x^2 + 2x + 5 = 0$
Discriminant: $\Delta = 4 - 20 = -16$
Roots: $-1 \pm 2i$

Example 3 — Complex Coefficients

./QuadCalc -cc 1,1 2,0 3,0

Equation: $(1+i)x^2 + 2x + 3 = 0$
Discriminant: $(-10.00 + 12.00i)$
Roots: $(-0.67 + 1.39i), (-1.33 - 0.39i)$

Example 4 — Square Root Coefficients

./QuadCalc -r 1 sqrt(2) -3

Equation: $x^2 + \sqrt{2}x - 3 = 0$
Discriminant: $\Delta = 2 + 12 = 14$
Roots: $x_1 \approx 1.29, x_2 \approx -2.00$

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📊 Visual Guide: Root Behavior

Real Discriminant (Δ):
   Δ > 0:  ●────────●     (two distinct real roots)
   Δ = 0:     ●           (one repeated real root)
   Δ < 0:     ●           (complex conjugate pair)
           ╱     ╲
          ●       ●       (on complex plane)

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🛠️ Project Structure

QuadCalculator/
├── includes/
│   ├── ColorMod.h
│   ├── Complex.h
│   ├── PPrintter.h
│   └── PPrintter.cpp   # currently in includes (odd)
├── src/
│   └── QuadCalculator.cpp
├── CMakeLists.txt
|── .gitignore
└── README.md

🔍 Technical Details

Numerical Precision

• Uses std::complex<double> for all calculations
• Handles edge cases like $a = 0$ (linear equation)
• Robust square root parsing with error checking

Algorithm

1. Parse input coefficients (real or complex, with sqrt support)
2. Validate that $a \neq 0$
3. Calculate discriminant $\Delta = b^2 - 4ac$
4. Compute roots using quadratic formula
5. Format output with appropriate precision

Error Handling

• Invalid coefficient formats
• Non-quadratic equations ($a = 0$)
• Malformed square root expressions
• Shell escaping issues

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🌟 Advanced Usage

Batch Processing

Create a script to solve multiple equations:

#!/bin/bash
echo "Solving multiple quadratics:"
./QuadCalc -r 1 -2 1    # (x-1)²
./QuadCalc -r 1 0 -4    # x² - 4
./QuadCalc -r 1 1 1     # x² + x + 1

Integration with Other Tools

Pipe results to analysis tools:

./QuadCalc -r 1 -3 2 | grep "Root" | awk '{print $3}'

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🤝 Contributing

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing-feature)
3. Make your changes and add tests
4. Commit your changes (git commit -m 'Add some amazing feature')
5. Push to the branch (git push origin feature/amazing-feature)
6. Open a Pull Request

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📚 References

• Quadratic Equation — Wikipedia
• Complex Numbers — Wikipedia
• Numerical Recipes in C++

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📄 License

MIT License—see the LICENSE file for details.

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🙏 Acknowledgments

• Thanks to the C++ community for modern language features
• Inspired by classic mathematical computation tools
• Built with ❤️ for students and engineers

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