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How to Solve Quadratic Equation in Python? (Program Examples)

Quadratic equations have their applications in various fields, from mathematics and physics to computer science and engineering. Understanding how to solve quadratic equation in Python not only enhances our problem-solving skills but also equips us with a versatile tool to tackle real-world challenges.

Whether you're a math enthusiast, a student, or a Python programmer, learning the Python program to solve quadratic equations opens up a realm of possibilities. In this digital era, where data-driven decision-making is vital, the ability to analyze and interpret quadratic equations becomes increasingly important.

The standard form of a quadratic equation is:

ax^2 + bx + c = 0

In this equation, "a," "b," and "c" are coefficients, and "x" is the variable.

Here are a few examples of quadratic equations in standard form:

x^2 - 5x + 6 = 0

2x^2 + 3x - 2 = 0

-4x^2 + 2x + 1 = 0

Here, we will explore different techniques and programs, and use Python to solve quadratic equations efficiently. 

Whether you're modeling the trajectory of a projectile, analyzing financial data, optimizing processes, or designing algorithms, the ability to solve quadratic equations empowers you to make accurate predictions, uncover hidden patterns, and make informed decisions.

So, let’s get started and know the quadratic equation program in Python.

Python Program to Solve Quadratic Equation

Code

# Simple quadratic equation program in Python

import cmath

# Input coefficients from the user
a = float(input("Enter the coefficient of x^2: "))
b = float(input("Enter the coefficient of x: "))
c = float(input("Enter the constant term: "))

# Calculate the discriminant
discriminant = (b ** 2) - (4 * a * c)

# Calculate the solutions
solution1 = (-b + cmath.sqrt(discriminant)) / (2 * a)
solution2 = (-b - cmath.sqrt(discriminant)) / (2 * a)

# Print the solutions
print("The solutions are:")
print("Solution 1:", solution1)
print("Solution 2:", solution2)

Output

Enter the coefficient of x^2: 3
Enter the coefficient of x: 3
Enter the constant term: 4
The solutions are:
Solution 1: (-0.5+1.0408329997330663j)
Solution 2: (-0.5-1.0408329997330663j)

Explanation

  • We first import the cmath module to handle complex numbers, as the solutions to a quadratic equation may involve complex numbers.

  • Next, we take input from the user for the coefficients of the quadratic equation (a, b, c).

  • Then, we calculate the discriminant using the formula: discriminant = b^2 - 4ac.

  • Next, we calculate the two solutions using the quadratic formula: (-b ± √(discriminant)) / (2a).

  • Finally, we print the solutions of the quadratic equation in Python.

Python Course

Quadratic Equation in Python Using Class

Code

# Solve quadratic equation in Python with class

import cmath

class QuadraticEquation:
    def __init__(self, a, b, c):
        self.a = a
        self.b = b
        self.c = c

    def calculate_discriminant(self):
        return (self.b ** 2) - (4 * self.a * self.c)

    def calculate_solutions(self):
        discriminant = self.calculate_discriminant()
        solution1 = (-self.b + cmath.sqrt(discriminant)) / (2 * self.a)
        solution2 = (-self.b - cmath.sqrt(discriminant)) / (2 * self.a)
        return solution1, solution2

# Input coefficients from the user
a = float(input("Enter the coefficient of x^2: "))
b = float(input("Enter the coefficient of x: "))
c = float(input("Enter the constant term: "))

# Create an instance of the QuadraticEquation class
equation = QuadraticEquation(a, b, c)

# Calculate and print the solutions of the quadratic equation
solutions = equation.calculate_solutions()
print("The solutions are:")
print("Solution 1:", solutions[0])
print("Solution 2:", solutions[1])

Output

Enter the coefficient of x^2: 1
Enter the coefficient of x: 5
Enter the constant term: 6
The solutions are:
Solution 1: (-2+0j)
Solution 2: (-3+0j)

Explanation

  • We define a class called QuadraticEquation. The constructor (__init__ method) initializes the coefficients of the quadratic equation (a, b, c) as instance variables.

  • We also define a method called calculate_discriminant within the class, which calculates the discriminant of the quadratic equation using the formula: discriminant = b^2 - 4ac.

  • The calculate_solutions method calculates the solutions of the quadratic equation using the quadratic formula: (-b ± √(discriminant)) / (2a). 

  • It first calls the calculate_discriminant method, then uses the discriminant to calculate the solutions.

  • We then take input from the user for the coefficients of the quadratic equation (a, b, c).

  • Next, we create an instance of the QuadraticEquation class, passing in the user-provided coefficients as arguments to the constructor.

  • Finally, we call the calculate_solutions method on the equation object to calculate the solutions of the quadratic equation, and we print the results.

Using a class provides a structured and object-oriented approach to solve the quadratic equation problem, encapsulating the coefficients and calculation methods within a single entity.

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Solve a Quadratic Equation in Python : Video