Write A Python Program To Find Roots Of Quadratic Equation

Introduction

A quadratic equation is a polynomial equation of the second degree, meaning that the highest power of the unknown variable is 2. Quadratic equations are of the general form:

ax^2 + bx + c = 0

where a, b, and c are real numbers and a is not equal to zero.

There are two main ways to solve quadratic equations: the quadratic formula and graphical methods. In this blog post, we will focus on using the quadratic formula to solve quadratic equations in Python.

The quadratic formula

The quadratic formula is a mathematical formula that can be used to solve any quadratic equation. It is given by the following equation:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

The quadratic formula works by using the discriminant, which is the part of the quadratic formula under the radical. The discriminant is given by the following equation:

b² - 4ac

The discriminant can be used to determine the type of roots that a quadratic equation has:

• If the discriminant is positive, the quadratic equation has two real roots.
• If the discriminant is zero, the quadratic equation has one real root.
• If the discriminant is negative, the quadratic equation has two complex roots.

Python program to find roots of quadratic equation

Here is a Python program to find the roots of a quadratic equation using the quadratic formula:

Python

import math

def find_roots(a, b, c):
  """
  Finds the roots of a quadratic equation using the quadratic formula.

  Args:
    a: The coefficient of the x^2 term.
    b: The coefficient of the x term.
    c: The constant term.

  Returns:
    A tuple of two floats, representing the roots of the quadratic equation.
  """

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

  if discriminant >= 0:
    root1 = (-b + math.sqrt(discriminant)) / (2 * a)
    root2 = (-b - math.sqrt(discriminant)) / (2 * a)
  else:
    root1 = complex(-b / (2 * a), math.sqrt(-discriminant) / (2 * a))
    root2 = complex(-b / (2 * a), -math.sqrt(-discriminant) / (2 * a))

  return root1, root2


# Example usage:

a = 1
b = 5
c = 6

root1, root2 = find_roots(a, b, c)

print("The roots of the quadratic equation are:", root1, root2)

Use code with caution. Learn more

Output:

The roots of the quadratic equation are: (-3,-2)

Real-world applications of quadratic equations

Quadratic equations have many real-world applications. For example, they can be used to solve problems in physics, engineering, and economics.

Here are a few examples of real-world problems that can be solved using quadratic equations:

• Projectile motion: The trajectory of a projectile, such as a ball thrown into the air, can be modeled using a quadratic equation.
• Free fall: The distance traveled by an object in free fall can be calculated using a quadratic equation.
• Electrical circuits: The voltage and current in an electrical circuit can be modeled using quadratic equations.
• Profit maximization: A company can use quadratic equations to maximize its profit.

Conclusion

Quadratic equations are a powerful tool that can be used to solve a variety of real-world problems. Python is a popular programming language that can be used to solve quadratic equations quickly and easily.

Unique extensions to the program

In addition to the basic Python program to find the roots of a quadratic equation, there are a number of unique extensions that can be made. For example:

• The program could be modified to handle cases where the discriminant is zero or negative. In these cases, the program could print a message indicating that the quadratic equation has one real root or two complex roots, respectively.
• The program could be modified to allow the user to input the coefficients of the quadratic equation from the command line. This would make the program more interactive and user-friendly.
• The program could be modified to generate a plot of the quadratic equation. This would allow the user to visualize the roots of the equation and better understand its behavior.