**Quadratic equation:**

Quadratic equation is derived from the Latin term “quadrates,” which means “square.” The equation of the Quadratic equation is:

ax2+bx+c=0

Here, “x” is an unknown that you must find, and “a”, “b”, and “c” are numbers such that “a” is not equal to 0. If a = 0, the equation becomes linear rather than quadratic.

The letters a, b, and c in the equation are known as coefficients.

where c= constant

- Java Program to Find the Roots of Quadratic Equation
- Python Program to Solve Quadratic Equation
- C Program to Find All Roots of Quadratic Equation

**Discrimination is defined as follows:**

discriminant = (b^2 – 4ac)

To determine the nature of the quadratic equation’s roots, we must first determine the value of its discriminant. For example, if we get a discriminant value more than 0 or can say positive, then the roots are “Distinct & Real.” The following are the different conditions of the discriminant and their respective values:

- Real and Distinct roots: if discriminant >0
- Roots are Equal: if discriminant =0
- Roots are Imaginary: if discriminant <0

## Check the Nature of Roots of a Quadratic Equation in Python

### Method #1: Using Mathematical Formula (Static Input)

**Approach:**

- Give the a value as static input and store it in a variable.
- Give the b value as static input and store it in another variable.
- Give the c value as static input and store it in another variable.
- Calculate the discriminant value of a quadratic equation using the above given mathematical formula and store it in a variable.
- Print the discriminant value of a quadratic equation
- Check if the above discriminant value is greater than 0 using the if conditional statement
- If it is true, then print the roots of a quadratic equation are Real
- Check if the above discriminant value is equal to 0 using the if conditional statement
- If it is true, then print the roots of a quadratic equation are Equal
- Check if the above discriminant value is less than 0 using the if conditional statement
- If it is true, then print the roots of a quadratic equation are Imaginary.
- The Exit of the Program.

**Below is the implementation:**

# Give the a value as static input and store it in a variable. gvn_a = 4 # Give the b value as static input and store it in another variable. gvn_b = 5 # Give the c value as static input and store it in another variable. gvn_c = 6 # Calculate the disciminant value of a quadratic equation using the above # given mathematical formula and store it in a variable. disciminant = gvn_b**2 -(4* gvn_a *gvn_c) # print the disciminant value of a quadratic equation print("The disciminant value of a quadratic equation = ", disciminant) # Check if the above discriminat value is greater than 0 using the if conditional statement if disciminant>0: # If it is true, then print the roots of a quadratic equation are Real print("The roots of a quadratic equation are Real") # Check if the above discriminant value is equal to 0 using the if conditional statement if disciminant==0: # If it is true, then print the roots of a quadratic equation are Equal print("The roots of a quadratic equation are Equal") # Check if the above discriminant value is less than 0 using the if conditional statement if disciminant<0: # If it is true, then print the roots of a quadratic equation are Imaginary print("The roots of a quadratic equation are Imaginary")

**Output:**

The disciminant value of a quadratic equation = -71 The roots of a quadratic equation are Imaginary

### Method #2: Using Mathematical Formula (User Input)

**Approach:**

- Give the a value as user input using the int(input()) function and store it in a variable.
- Give the b value as user input using the int(input()) function and store it in another variable.
- Give the c value as user input using the int(input()) function and store it in another variable.
- Calculate the discriminant value of a quadratic equation using the above given mathematical formula and store it in a variable.
- Print the discriminant value of a quadratic equation
- Check if the above discriminant value is greater than 0 using the if conditional statement
- If it is true, then print the roots of a quadratic equation are Real
- Check if the above discriminant value is equal to 0 using the if conditional statement
- If it is true, then print the roots of a quadratic equation are Equal
- Check if the above discriminant value is less than 0 using the if conditional statement
- If it is true, then print the roots of a quadratic equation are Imaginary.
- The Exit of the Program.

**Below is the implementation:**

# Give the a value as user input using the int(input()) function # and store it in a variable. gvn_a = int(input("Enter some random 'a' value = ")) # Give the b value as user input using the int(input()) function # and store it in another variable. gvn_b = int(input("Enter some random 'b' value = ")) # Give the c value as user input using the int(input()) function # and store it in another variable. gvn_c = int(input("Enter some random 'c' value = ")) # Calculate the disciminant value of a quadratic equation using the above # given mathematical formula and store it in a variable. disciminant = gvn_b**2 -(4* gvn_a *gvn_c) # print the disciminant value of a quadratic equation print("The disciminant value of a quadratic equation = ", disciminant) # Check if the above discriminat value is greater than 0 using the if conditional statement if disciminant>0: # If it is true, then print the roots of a quadratic equation are Real print("The roots of a quadratic equation are Real") # Check if the above discriminant value is equal to 0 using the if conditional statement if disciminant==0: # If it is true, then print the roots of a quadratic equation are Equal print("The roots of a quadratic equation are Equal") # Check if the above discriminant value is less than 0 using the if conditional statement if disciminant<0: # If it is true, then print the roots of a quadratic equation are Imaginary print("The roots of a quadratic equation are Imaginary")

**Output:**

Enter some random 'a' value = 1 Enter some random 'b' value = -5 Enter some random 'c' value = 6 The disciminant value of a quadratic equation = 1 The roots of a quadratic equation are Real