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Python Program to Solve Quadratic Equation

Tutorialsrack 22/04/2020 Python

In this Python Program, we will learn how to Solve Quadratic Equation. 

What is the Quadratic Equation?

In algebra, a quadratic equation is an equation that can be rearranged in standard form as

ax²+bx+c = 0

where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ax2 term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient, and the constant or free term.

A Quadratic Equation has at most two solutions, and they depend entirely upon the discriminant. If the discriminant > 0, then two distinct real roots exist for this equation. If discriminant = 0, two equal and real roots exist. Or if discriminant < 0, two distinct complex roots exist.

Here is the source code of the program to calculate the roots of a Quadratic Equation.

Program 1
# Python Program to Solve Quadratic Equation
# Solve the quadratic equation ax**2 + bx + c = 0

# Import complex math module
import cmath

a = 1
b = -7
c = 12

# To take coefficient input from the user
# a = float(input('Enter the Value of a: '))
# b = float(input('Enter the Value of b: '))
# c = float(input('Enter the Value of c: '))

# calculate the discriminant
d = (b**2) - (4*a*c)

# find two solutions
sol1 = (-b-cmath.sqrt(d))/(2*a)
sol2 = (-b+cmath.sqrt(d))/(2*a)

print('The solution is {0} and {1}'.format(sol1,sol2))
Python
Output

The solution is (3+0j) and (4+0j)

Another way to calculate the Quadratic Equation

Program 2
# Python Program to Solve Quadratic Equation

# Import Module
import math

a = 1
b = -7
c = 12

# To take coefficient input from the user
# a = float(input("Enter the Value of a: "))
# b = float(input("Enter the Value of b: "))
# c = float(input("Enter the Value of c: "))

discriminant = (b * b) - (4 * a * c)

if(discriminant > 0):
    root1 = (-b + math.sqrt(discriminant) / (2 * a))
    root2 = (-b - math.sqrt(discriminant) / (2 * a))
    print("Two Distinct Real Roots Exists: root1 = %.2f and root2 = %.2f" %(root1, root2))
elif(discriminant == 0):
    root1 = root2 = -b / (2 * a)
    print("Two Equal and Real Roots Exists: root1 = %.2f and root2 = %.2f" %(root1, root2))
elif(discriminant < 0):
    root1 = root2 = -b / (2 * a)
    imaginary = math.sqrt(-discriminant) / (2 * a)
    print("Two Distinct Complex Roots Exists: root1 = %.2f+%.2f and root2 = %.2f-%.2f" %(root1, imaginary, root2, imaginary))
Python
Output

Two Distinct Real Roots Exists: root1 = 7.50 and root2 = 6.50

In the above program, we import the cmath module to perform complex square root. 

First, we need to calculate the discriminant and then find the two solutions of the quadratic equation.

Tagged: Python Programming Python Programs Python Functions Python Programming Examples

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