This Python program computes the roots of a quadratic equation when coefficients **a, b, and c** are given as user input.

Imagine an engineer needs to determine the solutions of a quadratic equation that models the behavior of a physical system.

They can input the coefficients into the program to quickly and accurately calculate the roots of the equation.

```
import cmath
a = float(input("Enter the coefficient of x^2: "))
b = float(input("Enter the coefficient of x: "))
c = float(input("Enter the constant term: "))
# Calculate the discriminant
d = (b ** 2) - (4 * a * c)
# Calculate the solutions using the quadratic formula
sol1 = (-b - cmath.sqrt(d)) / (2 * a)
sol2 = (-b + cmath.sqrt(d)) / (2 * a)
print(f"The solutions are {sol1} and {sol2}.")
```

The program prompts the user to input the coefficients a, b, and c of the quadratic equation as floating-point numbers.

It calculates the discriminant of the equation using the formula** “d = b^2 – 4ac”**.

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

**Output:**

```
Enter the coefficient of x^2: 1
Enter the coefficient of x: -5
Enter the constant term: 6
The solutions are (3+0j) and (2+0j).
```

This example shows** the quadratic equation is x^2 – 5x + 6 = 0. **The program correctly calculates the two real roots of the equation as 3 and 2 and outputs them to the user.