In this article, We will be going to see How to find the roots of a quadratic equation: A*x^2 + B*x + C.

Example:

Input: Quadratic Equation: 1X^2 + 5X + 2
Output: The Roots of a Quadratic Equations are:  -0.4384 and -4.5616

for finding the roots we are using given below rules:

D = B^2 - 4*A*C

If D is greater than or equal to zero then real roots is exist and then it is calculated using :
root1 = -B + sqrt(D) / 2 * A and root2 =  -B - sqrt(D) / 2 * A.
If D is less than zero then the real roots not exist.

Now, let’s see the different ways to code this program:
Code 1: In this code, we are going to take inputs from user then type cast it into integer and then applying rules for finding roots.

# taking inputs from user and
# convert it into integer
var_a = int(input("Enter the A coefficient:"))
var_b = int(input("Enter the B coefficient:"))
var_c = int(input("Enter the C coefficient:"))

# show the quadratic equation
print("Quadratic Equation: "+ str(var_a)+ "X^2",
      "+", str(var_b) + "X", "+", var_c)

# calculate the value of D
# D = b^2 - 4ac
var_d = var_b * var_b - 4 * var_a * var_c

# check for real roots
# exists condition
if var_d >= 0 :

    # finding the roots and round of the
    # calculated values upto 4 places
    root1 = round(( -var_b + var_d ** (1/2) ) / 2 * var_a, 4)
    root2 = round(( -var_b - var_d ** (1/2) ) / 2 * var_a, 4)

    print("The Roots of a Quadratic Equations are: ",
          root1, "and", root2)

else :
    print("Imaginary Roots")

Output:

Enter the A coefficient:1
Enter the B coefficient:5
Enter the C coefficient:2
Quadratic Equation: 1X^2 + 5X + 2
The Roots of a Quadratic Equations are:  -0.4384 and -4.5616

Code 2:

# main code
if __name__ == "__main__" :
    
    # inputs given
    var_a = 1
    var_b = 5
    var_c = 2

    # show the quadratic equation
    print("Quadratic Equation: "+ str(var_a)+ "X^2",
          "+", str(var_b) + "X", "+", var_c)

    # calculate the value of D
    # D = b^2 - 4ac
    var_d = var_b * var_b - 4 * var_a * var_c

    # check for real roots
    # exists condition
    if var_d >= 0 :

        # finding the roots and round of the
        # calculated values upto 4 places
        root1 = round(( -var_b + var_d ** (1/2) ) / 2 * var_a, 4)
        root2 = round(( -var_b - var_d ** (1/2) ) / 2 * var_a, 4)

        print("The Roots of a Quadratic Equations are: ",
              root1, "and", root2)

    else :
        print("Imaginary Roots")

Output:

Quadratic Equation: 1X^2 + 5X + 2
The Roots of a Quadratic Equations are:  -0.4384 and -4.5616

Code 3: By creating a user defined function.

# Create a user defined function for
# finding roots of a quadratic equation
def findRoots(var_a, var_b, var_c) :

    # calculate the value of D
    # D = b^2 - 4ac
    var_d = var_b * var_b - 4 * var_a * var_c

    # check for real roots
    # exist condition
    if var_d >= 0 :

        # finding the roots and round of the
        # calculated values upto 4 places
        root1 = round(( -var_b + var_d ** (1/2) ) / 2 * var_a, 4)
        root2 = round(( -var_b - var_d ** (1/2) ) / 2 * var_a, 4)

        print("The Roots of a Quadratic Equations are: ",
              root1, "and", root2)

    else :
        print("Imaginary Roots")

# main code
if __name__ == "__main__" :
    
    # inputs given
    var_a = 1
    var_b = 5
    var_c = 2

    # show the quadratic equation
    print("Quadratic Equation: "+ str(var_a)+ "X^2",
          "+", str(var_b) + "X", "+", var_c)

    # function calling
    findRoots(var_a, var_b, var_c)

Output:

Quadratic Equation: 1X^2 + 5X + 2
The Roots of a Quadratic Equations are:  -0.4384 and -4.5616

Code 4: By creating a user defined function along with lambda function.

# Create a anonymous/lambda function for
# calculating the value of D
# D = b^2 - 4ac
find_d = lambda var_a, var_b, var_c : var_b * var_b - 4 * var_a * var_c

# Create a anonymous/lambda function for
# finding the roots and round of the
# calculated values upto 4 places
find_root1 = lambda var_a, var_b, var_d : round(( -var_b + var_d ** (1/2) ) / 2 * var_a, 4)

find_root2 = lambda var_a, var_b, var_d : round(( -var_b - var_d ** (1/2) ) / 2 * var_a, 4)

# Create a user defined function for
# finding roots of a quadratic equation
def findRoots(var_a, var_b, var_c) :

    # function calling
    var_d = find_d(var_a, var_b, var_c)

    # check for real roots
    # exist condition
    if var_d >= 0 :

        # function calling
        root1 = find_root1(var_a, var_b, var_d)
        root2 = find_root2(var_a, var_b, var_d)

        print("The Roots of a Quadratic Equations are: ",
              root1, "and", root2)

    else :
        print("Imaginary Roots")
        
# main code
if __name__ == "__main__" :
    
    # inputs given
    var_a = 1
    var_b = 5
    var_c = 2

    # show the quadratic equation
    print("Quadratic Equation: "+ str(var_a)+ "X^2",
          "+", str(var_b) + "X", "+", var_c)

    # function calling
    findRoots(var_a, var_b, var_c)

Output:

Quadratic Equation: 1X^2 + 5X + 2
The Roots of a Quadratic Equations are:  -0.4384 and -4.5616