Python program to solve quadratic equation (ax2+bx+c=0); In this tutorial, you will learn how to create a program in python to solve roots of a quadratic equation.

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is `ax² + bx + c = 0`

with a, b, and c being constants or numerical coefficients, and x is an unknown variable for example `6x² + 11x - 35 = 0`

.

The values of *x* that make the equation true are called **roots** of the equation Quadratic equations have 2 roots.

The term `b`

is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots.^{2}-4ac

- If the discriminant is greater than 0, the roots are real and different.
- If the discriminant is equal to 0, the roots are real and equal.
- If the discriminant is less than 0, the roots are complex and different.

## Python program to find the roots of an quadratic equation

Use the following steps and write a program to find and display roots of quadratic equation in python:

- Import the math module.
- Take inputs from the user.
- Use this formula
**X = b**2 – 4 * a * c**to solve a quadratic equation. - Next use conditional statements in the program.
- Print result.

import math a = float(input("Insert coefficient a: ")) b = float(input("Insert coefficient b: ")) c = float(input("Insert coefficient c: ")) discriminant = b**2 - 4 * a * c if discriminant >= 0: x_1=(-b+math.sqrt(discriminant))/2*a x_2=(-b-math.sqrt(discriminant))/2*a else: x_1= complex((-b/(2*a)),math.sqrt(-discriminant)/(2*a)) x_2= complex((-b/(2*a)),-math.sqrt(-discriminant)/(2*a)) if discriminant > 0: print("The function has two distinct real roots: {} and {}".format(x_1,x_2)) elif discriminant == 0: print("The function has one double root: ", x_1) else: print("The function has two complex (conjugate) roots: {} and {}".format(x_1,x_2))

#### Output

Insert coefficient a: 1 Insert coefficient b: 5 Insert coefficient c: 6 The function has two distinct real roots: -2.0 and -3.0

Explanation of the above python program

Import the built-in `math`

module to perform complex square root operation in the program. Then we are taking coefficient inputs from the user.

After that, calculate the discriminant using the `b`

formula, based on the result we have an if-else statement to compute the roots for complex conjugates we are using the python ^{2}-4ac`complex()`

method. Finally, Print out the result using string formatting.

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