Python Program For Solving Quadratic Equation (With Code)

In this tutorial, you will learn about the Python program for solving quadratic equation.

Quadratic equations are fundamental in mathematics and have various applications in real-life problem-solving.

By using a Python program to solve quadratic equations, you can automate the process and save time.

In this tutorial, we will walk you through the steps of writing a Python program to solve quadratic equations.

You’ll learn the necessary mathematical concepts, understand the logic behind the program, and get hands-on experience implementing the code.

A quadratic equation is a second-degree polynomial equation in a single variable, typically written in the form: ax² + bx + c = 0.

The coefficients a, b, and c represent real numbers, and x represents the variable.

The goal is to find the values of x that satisfy the equation.

The quadratic formula provides a way to solve any quadratic equation of the form ax² + bx + c = 0.

It is given by:

$x=\genfrac{}{}{0.1ex}{}{–b\pm \sqrt{b^2–4ac}}{2a}$

The quadratic formula involves the discriminant, which helps determine the nature of the roots.

Let’s delve into the implementation of a Python program to solve quadratic equations.

To solve quadratic equations using Python, we need to write a program that takes the coefficients a, b, and c as input and calculates the roots.

Here’s a step-by-step breakdown of the implementation:

Taking User Input

We begin by prompting the user to enter the coefficients a, b, and c.

We can use the input() function to gather the user’s input.

Let’s see how it’s done in Python:

a = float(input("Enter the coefficient a: "))
b = float(input("Enter the coefficient b: "))
c = float(input("Enter the coefficient c: "))

Calculating the Discriminant: Python Program For Solving Quadratic Equation

Next, we calculate the discriminant using the formula: D = b^2 – 4ac.

The discriminant helps us determine the nature of the roots.

We can use this information to guide the program’s logic.

Here’s the Python code for calculating the discriminant:

D = b**2 - 4*a*c

Determining the Nature of Roots

Before solving the equation, we need to check the discriminant’s value to determine the nature of the roots. There are three possible scenarios:

• If D > 0, the equation has two distinct real roots.
• If D = 0, the equation has one real root (a repeated root).
• If D < 0, the equation has two complex roots.

Solving the Quadratic Equation: Python Program For Solving Quadratic Equation

Based on the discriminant’s value, we can write conditional statements to solve the quadratic equation accordingly. Let’s explore the different scenarios and write the corresponding Python code.

Case 1: Two Distinct Real Roots

When D > 0, the quadratic equation has two distinct real roots.

We can use the quadratic formula to calculate these roots.

The Python code for this case is as follows:

x1 = (-b + math.sqrt(D)) / (2*a)
x2 = (-b - math.sqrt(D)) / (2*a)

Case 2: One Real Root (Repeated Root)

When D = 0, the quadratic equation has one real root. In this case, the roots will be identical.

The Python code is as follows:

x = -b / (2*a)

Case 3: Two Complex Roots

When D < 0, the quadratic equation has two complex roots.

Complex roots consist of a real and an imaginary part.

To handle this scenario, we can use the concept of complex numbers in Python.

Here’s the code:

x1 = (-b + cmath.sqrt(D)) / (2*a)
x2 = (-b - cmath.sqrt(D)) / (2*a)

Handling Complex Roots: Python Program For Solving Quadratic Equation

To handle complex roots, we need to import the cmath module, which provides functions for working with complex numbers in Python.

By using cmath.sqrt(), we can calculate the square root of a negative number and obtain a complex result.

It’s important to test the program with different inputs to ensure its accuracy and reliability.

You can try various combinations of coefficients a, b, and c and verify if the program produces the correct results.

Python Program For Solving Quadratic Equation

import math

def solve_quadratic_equation(a, b, c):
    # Calculate the discriminant
    D = b**2 - 4*a*c

    # Determine the nature of roots
    if D > 0:
        # Two distinct real roots
        x1 = (-b + math.sqrt(D)) / (2*a)
        x2 = (-b - math.sqrt(D)) / (2*a)
        return x1, x2
    elif D == 0:
        # One real root (repeated root)
        x = -b / (2*a)
        return x
    else:
        # Two complex roots
        x1 = (-b + cmath.sqrt(D)) / (2*a)
        x2 = (-b - cmath.sqrt(D)) / (2*a)
        return x1, x2

# Taking user input
a = float(input("Enter the coefficient a: "))
b = float(input("Enter the coefficient b: "))
c = float(input("Enter the coefficient c: "))

# Solve the quadratic equation
roots = solve_quadratic_equation(a, b, c)

# Display the results
if isinstance(roots, tuple):
    print("The quadratic equation has two distinct real roots:")
    print("x1 =", roots[0])
    print("x2 =", roots[1])
else:
    print("The quadratic equation has one real root (repeated root):")
    print("x =", roots)

Output

The expected roots for this equation are x1 = 3 and x2 = 0.5.

You can run the program on our free online python compiler to verify the results.

How can I solve a quadratic equation using Python?

You can solve a quadratic equation using a Python program.

By implementing the quadratic formula and considering different scenarios based on the discriminant, you can accurately calculate the roots.

Can Python handle complex roots in quadratic equations?

Yes, Python can handle complex roots.

By using the cmath module, you can work with complex numbers and calculate the roots of quadratic equations with negative discriminates.

What if I enter non-numeric values for the coefficients?

If you enter non-numeric values for the coefficients, Python will raise a ValueError indicating that the input is invalid.

Make sure to provide valid numerical inputs for the program to function correctly.

Are there any limitations to this Python program?

This Python program assumes the input coefficients are real numbers and only solves quadratic equations.

It does not handle other types of equations or non-quadratic expressions.

Can I use this program to solve quadratic equations in other programming languages?

While the logic remains the same, the syntax may differ across programming languages.

However, the quadratic formula and the concepts involved can be implemented in various programming languages to solve quadratic equations.

In this tutorial, we explored how to solve quadratic equations using a Python program.

We covered the quadratic formula, the discriminant, and the logic behind handling different scenarios.

By implementing the code provided and testing it with various inputs, you can efficiently solve quadratic equations and obtain the roots.

Python’s flexibility and mathematical capabilities make it an ideal choice for automating quadratic equation solving.

Now you can confidently write Python programs to solve quadratic equations and apply this knowledge to real-life problem-solving.