Solving Quadratic Equations with Python

Quadratic equations are a type of polynomial equation that have been studied for centuries. They have applications in various fields such as physics, engineering, and economics. A quadratic equation is of the form ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. In this blog post, we will write a Python code to solve quadratic equations.

Python is a powerful programming language that is widely used in scientific computing and data analysis. It provides built-in support for complex numbers and mathematical operations, making it an ideal choice for solving quadratic equations.

To solve a quadratic equation using Python, we need to first import the cmath module, which provides support for complex math calculations. We then define the values of a, b, and c for our equation.

import cmath

# Solving a quadratic equation ax^2 + bx + c = 0
a = 1
b = 5
c = 6

Next, we calculate the discriminant d of the quadratic equation using the formula d = b^2 - 4ac. The discriminant tells us the nature of the roots of the quadratic equation. If d > 0, the equation has two real roots, if d = 0, the equation has one real root (a repeated root), and if d < 0, the equation has two complex roots.

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

We then calculate the two solutions of the quadratic equation using the formula (-b ± sqrt(d))/(2a). We can use the cmath.sqrt() function to calculate the square root of a complex number.

# find two solutions
sol1 = (-b-cmath.sqrt(d))/(2*a)
sol2 = (-b+cmath.sqrt(d))/(2*a)

Finally, we print out the solutions using the print() function.

# print the solutions
print('The solutions are {0} and {1}'.format(sol1,sol2))

Putting it all together, we get the following Python code to solve quadratic equations:

import cmath

# Solving a quadratic equation ax^2 + bx + c = 0
a = 1
b = 5
c = 6

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

# find two solutions
sol1 = (-b-cmath.sqrt(d))/(2*a)
sol2 = (-b+cmath.sqrt(d))/(2*a)

# print the solutions
print('The solutions are {0} and {1}'.format(sol1,sol2))

If we run this code, we get the following output:

The solutions are (-3+0j) and (-2+0j)

which are the two roots of the equation x^2 + 5x + 6 = 0.

Solving quadratic equations using Python is a simple and straightforward process. Python provides built-in support for complex math calculations and makes it easy to work with mathematical formulas and equations.