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Python Solve Quadratic Equation

Python Solve Quadratic Equation

Given a quadratic equation the task is solve the equation or find out the roots of the equation. Standard form of quadratic equation is $$ax^2+ bx + c =0$$ where, $a, b$, and $c$ are coefficient and real numbers and also $a \ne 0$ 0. If $a$ is equal to $0$ that equation is not valid quadratic equation.

SGK, sách ôn thi, sách tham khảo giá rẻ

See more: Hướng dẫn lập trình Python – Python Guide

1. Python Solve Quadratic Equation Using the Direct Formula

Using the below quadratic formula we can find the root of the quadratic equation.

Let $\Delta =b^2-4ac$, then:

  • If $b^2 – 4ac<0$, then roots are complex (not real).
  • If $b^2 – 4ac=0$, then roots are real and both roots are same $x=\frac{-b}{2a}$.
  • If $b^2 – 4ac>0$, then roots are real and different $$ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$
# Python program to find roots of quadratic equation 
import math 


# function for finding roots 
def equationroots(): 

   a = float(input('Enter coefficient a: '))
   while a == 0:
      print("Coefficient a can not equal 0")
      a = float(input('Enter coefficient a: '))
   b = float(input('Enter coefficient b: '))
   c = float(input('Enter coefficient c: '))
   
   # calculating dcriminant using formula 
   d = b * b - 4 * a * c 
   
   # checking condition for dcriminant 
   if d > 0: 
      print("Your equation has real and different roots:") 
      print((-b + math.sqrt(d))/(2 * a)) 
      print((-b - math.sqrt(d))/(2 * a)) 
   
   elif d == 0: 
      print("Your equation has real and same roots:") 
      print(-b / (2 * a)) 
   
   # when dcriminant is less than 0 
   else: 
      print("Your equation has complex roots:") 
      print(- b / (2 * a), " +", math.sqrt(-d),'i') 
      print(- b / (2 * a), " -", math.sqrt(-d),'i') 


equationroots() 

2. Python Solve Quadratic Equation Using the Complex Math Module

First, we have to calculate the discriminant and then find two solution of quadratic equation using cmath module.

SGK, sách ôn thi, sách tham khảo giá rẻ

cmath module — Mathematical functions for complex numbers — provides access to mathematical functions for complex numbers. The functions in this module accept integers, floating-point numbers or complex numbers as arguments. They will also accept any Python object that has either a __complex__() or a __float__() method: these methods are used to convert the object to a complex or floating-point number, respectively, and the function is then applied to the result of the conversion.

# Python program to find roots of quadratic equation 
import cmath 


# function for finding roots 
def equationroots(): 

   a = float(input('Enter coefficient a: '))
   while a == 0:
      print("Coefficient a can not equal 0")
      a = float(input('Enter coefficient a: '))
   b = float(input('Enter coefficient b: '))
   c = float(input('Enter coefficient c: '))
   
   # calculating dcriminant using formula 
   d = b * b - 4 * a * c 
   
   if d == 0: 
      print("Your equation has real and same roots:") 
      print(-b / (2 * a)) 
   
   # when dcriminant is not equal 0 
   else: 
      print("Your equation has complex roots:") 
      print(- b / (2 * a), " +", cmath.sqrt(d)) 
      print(- b / (2 * a), " -", cmath.sqrt(d)) 


equationroots() 

input()

 


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