In algebra, Discriminant helps us deduce 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:
ax^2+bx+c
Here the discriminant of the equation is calculated using the formula:
b^2-4ac
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 a 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++
#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";
}
}
int main(){
int a = 20, b = 30, c = 10;
discriminant(a, b, c);
return 0;
}
|
Java
public class Discriminant{
static int disc(int a, int b, int c){
int dis = (int)Math.pow(b,2) - (4*a*c);
return dis;
}
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
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')
a = 20
b = 30
c = 10
discriminant(a, b, c)
|
C#
using System;
class GFG
{
static int disc(int a,
int b, int c)
{
int dis = (int)Math.Pow(b, 2) -
(4 * a * c);
return dis;
}
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");
}
}
}
|
PHP
<?php
function discriminant($a, $b, $c)
{
$discriminant = ($b * $b) - (4 * $a * $c);
if($discriminant > 0)
{
echo "Discriminant is ", $discriminant,
" which is Positive\n";
echo "Hence Two Solutions";
}
else if($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";
}
}
$a = 20;
$b = 30;
$c = 10;
discriminant($a, $b, $c);
?>
|
Javascript
<script>
function disc(a , b , c) {
var dis = parseInt( Math.pow(b, 2) - (4 * a * c));
return dis;
}
var a = 20;
var b = 30;
var c = 10;
var discriminant = disc(a, b, c);
if (discriminant > 0) {
document.write("Discriminant is " + discriminant + " which is Positive<br/>");
document.write("Hence Two Solutions");
} else if (discriminant == 0) {
document.write("Discriminant is " + discriminant + " which is Zero<br/>");
document.write("Hence One Solution");
} else {
document.write("Discriminant is " + discriminant + " which is Negative<br/>");
document.write("Hence No Real Solutions");
}
</script>
|
Output:
Discriminant is 100 which is Positive
Hence Two Solutions
Time Complexity: O(1) since constant operations are being performed
Auxiliary Space: O(1), since no extra space has been taken.
This article is contributed by Chinmoy Lenka. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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