#!/bin/bash

# Equation solver in Bash
solve_equation() {
    local a=$1
    local b=$2
    local c=$3
    
    echo "Solving: ${a}x² + ${b}x + ${c} = 0"
    
    # Check if bc is available for floating point math
    if ! command -v bc &> /dev/null; then
        echo "Error: bc calculator is required but not installed. Install with: sudo apt install bc"
        return 1
    fi
    
    # Linear equation (a = 0)
    if [ "$(echo "$a == 0" | bc -l)" -eq 1 ]; then
        if [ "$(echo "$b == 0" | bc -l)" -eq 1 ]; then
            if [ "$(echo "$c == 0" | bc -l)" -eq 1 ]; then
                echo "Infinite solutions"
            else
                echo "No solution"
            fi
        else
            local x=$(echo "scale=4; -($c) / $b" | bc)
            echo "Linear equation: x = $x"
        fi
        return
    fi
    
    # Quadratic equation
    local discriminant=$(echo "scale=4; $b*$b - 4*$a*$c" | bc)
    echo "Discriminant = $discriminant"
    
    if [ "$(echo "$discriminant > 0" | bc -l)" -eq 1 ]; then
        local x1=$(echo "scale=4; (-$b + sqrt($discriminant)) / (2*$a)" | bc)
        local x2=$(echo "scale=4; (-$b - sqrt($discriminant)) / (2*$a)" | bc)
        echo "Two real roots: x₁ = $x1, x₂ = $x2"
    elif [ "$(echo "$discriminant == 0" | bc -l)" -eq 1 ]; then
        local x=$(echo "scale=4; -$b / (2*$a)" | bc)
        echo "One real root: x = $x"
    else
        local real_part=$(echo "scale=4; -$b / (2*$a)" | bc)
        local imag_part=$(echo "scale=4; sqrt(-$discriminant) / (2*$a)" | bc)
        echo "Complex roots: x₁ = $real_part + ${imag_part}i, x₂ = $real_part - ${imag_part}i"
    fi
}

# Test cases
echo "=== BASH EQUATION SOLVER ==="
solve_equation 1 -3 2
echo "---"
solve_equation 1 2 1
echo "---"
solve_equation 1 0 1
echo "---"
solve_equation 0 2 -4
echo "---"
solve_equation 0 0 0
echo "---"
solve_equation 0 0 5