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Calculate the Discriminant Value


In algebra, Discriminant helps us in deducing various properties of the roots of a polynomial or polynomial function without even computing them. Let’s look at this general quadratic polynomial of degree two:

ax2 + bx + c

Here the discriminant of the equation is calculated using the formula:

b2 – 4ac



Now we can deduce the following properties:

  • If the discriminant is equal to zero then the polynomial has equal roots i.e., a=b.
  • If the discriminant is positive and the coefficients are real, then the polynomial has two real roots.

Here are few conditions that we must keep in mind while programming and making deductions from the discriminant:

  • If the discriminant is equal to zero then one solution is possible.
  • If the discriminant is positive then two solutions are possible.
  • If the discriminant is negative then no real solutions are possible.

 
Examples:

Input:
a = 20
b = 30
c = 10
Explanation:
(30**2) - (4*20*10) 
Output:
Discriminant is 100 which is positive
Hence Two solutions

Input:
a = 9
b = 7
c = 12
Explanation:
(30**2) - (4*20*10) 
Output:
Discriminant is -383 which is negative
Hence no real solutions



C++

// CPP program to calculate Discriminant
#include <bits/stdc++.h>
  
using namespace std;
  
void discriminant(int a, int b, int c){
  
    int discriminant = (b*b) - (4*a*c);
    if(discriminant > 0){
        cout<<"Discriminant is "<<discriminant
            <<" which is Positive"<<endl;
              
        cout<<"Hence Two Solutions";
    }
    else if(discriminant == 0){
        cout<<"Discriminant is "<<discriminant
            <<" which is Zero"<<endl;
              
        cout<<"Hence One Solution";
    }
    else if(discriminant < 0){
        cout<<"Discriminant is "<<discriminant
            <<" which is Negative"<<endl;
              
        cout<<"Hence No Real Solutions";
    }
}
  
// Driver Code
int main(){
    int a = 20, b = 30, c = 10;
  
    // function call to print discriminant
    discriminant(a, b, c);
    return 0;
}
  
// This code is contributed by
// Sanjit_Prasad

/div>

Java

// Java program to calculate discriminant
public class Discriminant{
      
    // function to calculate discriminant
    static int disc(int a, int b, int c){
        int dis = (int)Math.pow(b,2) - (4*a*c);
        return dis;
    }
  
    // Driver Code
    public static void main(String args[]){
        int a=20;
        int b=30;
        int c=10;
        int discriminant = disc(a, b, c);
        if (discriminant > 0){
            System.out.println("Discriminant is " + discriminant 
                    + " which is Positive");
            System.out.println("Hence Two Solutions");
        }
        else if (discriminant == 0){
            System.out.println("Discriminant is " + discriminant
                    + " which is Zero");
            System.out.println("Hence One Solution");
        }
        else {
            System.out.println("Discriminant is "+ discriminant 
                    + " which is Negative");
            System.out.println("Hence No Real Solutions");
        }
    }
}

Python3

# Python program to calculate Discriminant
  
def discriminant(a, b, c):
  
    discriminant = (b**2) - (4*a*c)
    if discriminant > 0:
          
        print('Discriminant is', discriminant,
                "which is Positive")
                  
        print('Hence Two Solutions')
          
    elif discriminant == 0:
          
        print('Discriminant is', discriminant, 
                "which is Zero")
                  
        print('Hence One Solution')
          
    elif discriminant < 0:
          
        print('Discriminant is', discriminant, 
                "which is Negative")
                  
        print('Hence No Real Solutions')
  
# Driver Code
a = 20
b = 30
c = 10
discriminant(a, b, c)

C#

// C# program to calculate
// discriminant
using System;
  
class GFG
{
  
// function to calculate
// discriminant
static int disc(int a, 
                int b, int c)
{
    int dis = (int)Math.Pow(b, 2) - 
                    (4 * a * c);
    return dis;
}
      
// Driver Code
public static void Main()
{
    int a = 20;
    int b = 30;
    int c = 10;
    int discriminant = disc(a, b, c);
    if (discriminant > 0)
    {
        Console.WriteLine("Discriminant is "
                                discriminant + 
                        " which is Positive");
        Console.WriteLine("Hence Two Solutions");
    }
      
    else if (discriminant == 0)
    {
        Console.WriteLine("Discriminant is "
                                discriminant + 
                            " which is Zero");
        Console.WriteLine("Hence One Solution");
    }
      
    else
    {
        Console.WriteLine("Discriminant is "
                            discriminant + 
                    " which is Negative");
        Console.WriteLine("Hence No Real Solutions");
    }
}
}
  
// This code is contributed
// by anuj_67.

PHP

<?php
// PHP program to calculate Discriminant
  
function discriminant($a, $b, $c)
{
      
    $discriminant = ($b * $b) - (4 * $a * $c);
    if($discriminant > 0)
    {
        echo "Discriminant is ", $discriminant
             " which is Positive ";
        echo "Henco Two Solutions";
    }
      
    else if($discriminant == 0)
    
        echo "Discriminant is ", $discriminant
             " which is Zero "
        echo "Hence One Solution"
    
      
    else if($discriminant < 0)
    
        echo "Discriminant is ", $discriminant
             " which is Negative "
              
        echo "Hence No Real Solutions"
    
}
  
// Driver code
$a = 20;
$b = 30;
$c = 10;
  
// function call to print discriminant
discriminant($a, $b, $c);
  
// This code is contributed 
// by Shashank_Sharma
?>

Output:

Discriminant is 100 which is Positive
Hence Two Solutions

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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