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 |
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 = 20b = 30c = 10discriminant(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 ", $discriminant, " which is Positive\n"; echo "Henco Two Solutions"; } else if($discriminant == 0) { echo "Discriminant is ", $discriminant, " which is Zero\n"; echo "Hence One Solution"; } else if($discriminant < 0) { echo "Discriminant is ", $discriminant, " which is Negative\n"; 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
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