Python Program - Find Roots of a Quadratic Equation

A standard form of a quadratic equation is:

ax² + bx + c = 0

Where:

a, b and c are real numbers and a ≠ 0.

Roots of the equation are:

For Example:

The roots of equation x² + 5x + 4 = 0 is

The roots of the equation will be imaginary if D = b² - 4ac < 0. For example - the roots of equation x² + 4x + 5 = 0 will be

Method 1: Calculate roots of a Quadratic equation

In the example below, a function called roots is created which takes a, b and c as arguments to calculate the roots of the equation ax² + bx + c = 0.

import math

def roots(a, b, c):
  D = b*b - 4*a*c
  if D >= 0:
    x1 = (-b + math.sqrt(D))/(2*a)
    x2 = (-b - math.sqrt(D))/(2*a)
    print("Roots are:",x1,",",x2)
  else:
    x1 = -b/(2*a)
    x2 = math.sqrt(-D)/(2*a)
    print("Roots are:",x1,"±",x2,"i")

print("Equation is x*x+5x+4=0")
roots(1,5,4)
print("\nEquation is x*x+4x+5=0")
roots(1,4,5)

The above code will give the following output:

Equation is x*x+5x+4=0
Roots are: -1.0 , -4.0

Equation is x*x+4x+5=0
Roots are: -2.0 ± 1.0 i

Method 2: Using cmath Module

The above problem also be solved by importing cmath module which can handle the complex number.

import cmath

def roots(a, b, c):
  D = b*b - 4*a*c
  x1 = (-b + cmath.sqrt(D))/(2*a)
  x2 = (-b - cmath.sqrt(D))/(2*a)
  print("Roots are:",x1,"and",x2)

print("Equation is x*x+5x+4=0")
roots(1,5,4)
print("\nEquation is x*x+4x+5=0")
roots(1,4,5)

The above code will give the following output:

Equation is x*x+5x+4=0
Roots are: (-1+0j) and (-4+0j)

Equation is x*x+4x+5=0
Roots are: (-2+1j) and (-2-1j)