Program to Find Roots of a Quadratic Equation in Python

Finding Roots of a Quadratic Equation

A quadratic equation is in the form ax² + bx + c = 0. The roots of this equation can be real or complex depending on the discriminant (D = b² - 4ac).

We will explore three different methods to find the roots of a quadratic equation in Python.

Method 1: Using the Quadratic Formula

This method uses the quadratic formula: x = (-b ± sqrt(b² - 4ac)) / (2a).

import math

def find_roots(a, b, c):
    discriminant = b**2 - 4*a*c
    if discriminant > 0:
        root1 = (-b + math.sqrt(discriminant)) / (2 * a)
        root2 = (-b - math.sqrt(discriminant)) / (2 * a)
        print(f"Real and Distinct Roots: {root1}, {root2}")
    elif discriminant == 0:
        root = -b / (2 * a)
        print(f"Real and Equal Roots: {root}")
    else:
        real_part = -b / (2 * a)
        imag_part = math.sqrt(-discriminant) / (2 * a)
        print(f"Complex Roots: {real_part} + {imag_part}i, {real_part} - {imag_part}i")

# Get user input
a, b, c = map(int, input("Enter coefficients a, b, and c: ").split())
find_roots(a, b, c)
            

Method 2: Using Factorization

Factorization is an alternative method where we break the middle term to find the roots.

def find_roots_factorization(a, b, c):
    found = False
    for i in range(-100, 101):
        for j in range(-100, 101):
            if i * j == a * c and i + j == b:
                print(f"Roots are: {-j}/{a} and {-i}/{a}")
                found = True
                return
    if not found:
        print("Cannot be factorized easily.")

# Get user input
a, b, c = map(int, input("Enter coefficients a, b, and c: ").split())
find_roots_factorization(a, b, c)
            

Method 3: Using Recursion

This method recursively calculates the discriminant and finds the roots.

def find_roots_recursive(a, b, c, d):
    if d > 0:
        root1 = (-b + math.sqrt(d)) / (2 * a)
        root2 = (-b - math.sqrt(d)) / (2 * a)
        print(f"Real and Distinct Roots: {root1}, {root2}")
    elif d == 0:
        root = -b / (2 * a)
        print(f"Real and Equal Roots: {root}")
    else:
        real_part = -b / (2 * a)
        imag_part = math.sqrt(-d) / (2 * a)
        print(f"Complex Roots: {real_part} + {imag_part}i, {real_part} - {imag_part}i")

def calculate_discriminant(a, b, c):
    d = b**2 - 4*a*c
    find_roots_recursive(a, b, c, d)

# Get user input
a, b, c = map(int, input("Enter coefficients a, b, and c: ").split())
calculate_discriminant(a, b, c)