Python Program to Find the Roots of a Quadratic Equation

1. Introduction

Solving quadratic equations is a fundamental problem in algebra. In Python, we can create a program to find the roots of a quadratic equation of the form ax^2 + bx + c = 0 using the quadratic formula.

The roots of a quadratic equation ax^2 + bx + c = 0 are given by the formulas:

(-b + sqrt(b^2 - 4ac)) / (2a)

(-b - sqrt(b^2 - 4ac)) / (2a)

These roots can be real or complex numbers depending on the discriminant b^2 - 4ac.

2. Program Steps

1. Define the coefficients a, b, and c of the quadratic equation.

2. Calculate the discriminant b^2 - 4ac.

3. Determine the nature of the roots based on the discriminant.

4. Calculate and print the roots using the appropriate formula.

3. Code Program

import cmath  # Import complex math module

# Function to calculate roots of quadratic equation
def find_roots(a, b, c):
    # Calculate the discriminant
    discriminant = cmath.sqrt(b**2 - 4*a*c)
    # Calculate two solutions
    root1 = (-b + discriminant) / (2*a)
    root2 = (-b - discriminant) / (2*a)
    return root1, root2

# Coefficients of the quadratic equation
a_coeff = 1
b_coeff = 5
c_coeff = 6
# Calculate the roots
root_1, root_2 = find_roots(a_coeff, b_coeff, c_coeff)
# Print the results
print(f"The roots of the quadratic equation are: {root_1} and {root_2}")

Output:

The roots of the quadratic equation are: (-2+0j) and (-3+0j)

Explanation:

1. cmath library is imported to handle complex square roots.

2. find_roots function is defined to take the coefficients a, b, and c as arguments.

3. The discriminant is calculated using b2 - 4ac, and cmath.sqrt is used to handle complex results.

4. root1 and root2 are calculated using the quadratic formula.

5. The coefficients of the equation a_coeff, b_coeff, and c_coeff are defined with the values 1, 5, and 6, representing ax^2 + bx + c.

6. The find_roots function is called with these coefficients and returns two roots.

7. The roots are printed, which are (-2+0j) and (-3+0j) indicating two real roots at -2 and -3.

8. The output is formatted with an f-string to clearly present the roots.