Quadratic Formula Python | Python Program To Solve Quadratic Equation

Here given a quadratic equation the task is to solve the equation or find out the roots of the equation. The standard form of a quadratic equation is –

ax2 + bx + c
where,
a, b, and c are coefficient and real numbers and also a ≠ 0.
If a is equal to 0 that equation is not valid quadratic equation.

Examples Of Quadratic Equation:

Input :a = 1, b = 2, c = 1 
Output : 
Roots are real and same
-1.0

Input :a = 2, b = 2, c = 1
Output :
Roots are complex
-0.5  + i 2.0
-0.5  - i 2.0

Input :a = 1, b = 10, c = -24 
Output : 
Roots are real and different
2.0
-12.0

Method 1: Using the direct formula

So here we describes different cases of Quadratic Equation:

If b*b < 4*a*c, then roots are complex
(not real).
For example roots of x2 + x + 1, roots are
-0.5 + i1.73205 and -0.5 - i1.73205

If b*b == 4*a*c, then roots are real 
and both roots are same.
For example, roots of x2 - 2x + 1 are 1 and 1

If b*b > 4*a*c, then roots are real 
and different.
For example, roots of x2 - 7x - 12 are 3 and 4

Below program illustrate the quadratic equation in Python:

# Python program to find roots of quadratic equation
import math


# function for finding roots
def equationroots( a, b, c):

	# calculating discriminant using formula
	dis = b * b - 4 * a * c
	sqrt_val = math.sqrt(abs(dis))
	
	# checking condition for discriminant
	if dis > 0:
		print(" real and different roots ")
		print((-b + sqrt_val)/(2 * a))
		print((-b - sqrt_val)/(2 * a))
	
	elif dis == 0:
		print(" real and same roots")
		print(-b / (2 * a))
	
	# when discriminant is less than 0
	else:
		print("Complex Roots")
		print(- b / (2 * a), " + i", sqrt_val)
		print(- b / (2 * a), " - i", sqrt_val)

# Driver Program
a = 1
b = 10
c = -24

# If a is 0, then incorrect equation
if a == 0:
		print("Input correct quadratic equation")

else:
	equationroots(a, b, c)

Output:

real and different roots
2.0
-12.0

Method-2: Using Complex Math Module

# import complex math module
import cmath

a = 1
b = 4
c = 2

# calculating the discriminant
dis = (b**2) - (4 * a*c)

# find two results
ans1 = (-b-cmath.sqrt(dis))/(2 * a)
ans2 = (-b + cmath.sqrt(dis))/(2 * a)

# printing the results
print('The roots are')
print(ans1)
print(ans2)

Output:

The roots are
(-3.414213562373095+0j)
(-0.5857864376269049+0j)

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