Python Program to Solve Quadratic Equation

Introduction

Solving quadratic equations is a fundamental problem in algebra. A quadratic equation takes the form (ax^2 + bx + c = 0), where (a), (b), and (c) are constants, and (a \neq 0). Python, with its robust libraries and straightforward syntax, simplifies the process of finding the roots of these equations.

In this article, you will learn how to solve quadratic equations using Python. Through practical examples, explore how to determine the type of solutions you might expect (real or complex) and how to compute these solutions accurately.

Solving Quadratic Equations in Python

Preparing to Solve the Equation

1. Import the necessary module.

2. Define the coefficients (a), (b), and (c).

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   import cmath
   
   a = 1
   b = 5
   c = 6

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   Here, cmath is used for complex numbers because the solutions might need to handle square roots of negative numbers.

Calculating the Discriminant

1. Compute the discriminant using (b^2 - 4ac).

2. The discriminant helps determine the nature of the roots.

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

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   A positive discriminant indicates two real and distinct roots, zero discriminant indicates exactly one real root, and a negative discriminant suggests two complex roots.

Finding the Roots

1. Calculate the two solutions using the quadratic formula.

2. Apply the formula based on the discriminant.

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   root1 = (-b - cmath.sqrt(discriminant)) / (2 * a)
   root2 = (-b + cmath.sqrt(discriminant)) / (2 * a)

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   Regardless of the discrimant's sign, roots are computed using complex math functions to accommodate all cases.

Displaying the Results

1. Output the roots to the console.

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   print("The roots are {0} and {1}".format(root1, root2))

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   This final step presents the roots, which may either be real numbers or complex numbers if the discriminant was negative.

Conclusion

Solving a quadratic equation with Python is efficient and straightforward. By leveraging Python's cmath module, you can handle both real and complex roots with ease. This method provides a powerful way to tackle quadratic equations, ensuring that you always arrive at the correct roots regardless of the discriminant. With these examples, you enhance your mathematical problem-solving skills using Python programming.