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 b2-4ac is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots.

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

Problem Definition

Create a Python program to find the roots of a quadratic equation.

Program

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

In the program first, we are importing the built-in math module to perform complex square root operation later in the program. Then we are taking coefficient inputs from the user.

Next, we are calculating the discriminant using the b2-4ac formula, based on the result we have a conditional statement to compute the roots for complex conjugates we are using the python complex() method. Finally, we are printing out the result using string formatting.