Program to find number of solutions in Quadratic Equation

Given an equation ax^{2}\pm bx\pm c=0   with value a, b, and c, where a and b is any value and c is constant, find how many solutions thus this quadratic equation have?
Examples: 
 

Input : 2x^{2}+5x+2=0Output : 2 solutionsInput : x^{2}+x+1=0Output : no solution

Solution: 
To check whether the equation has a solution or not, quadratic formula for discriminant is used.
 

The formula is given as, b^{2}-4ac 

Respective conditions are given as, 
 

• if the discriminant is positive b^{2}-4ac> 0   , then the quadratic equation has two solutions.
• if the discriminant is equal b^{2}-4ac= 0   , then the quadratic equation has one solution.
• if the discriminant is negative b^{2}-4ac< 0   , then the quadratic equation has no solution.

Programs: 
 

// C++ Program to find the solutions of specified equations
#include <iostream>
using namespace std;

// Method to check for solutions of equations
void checkSolution(int a, int b, int c)
{

    // If the expression is greater than 0, then 2 solutions
    if (((b * b) - (4 * a * c)) > 0)
        cout << "2 solutions";

    // If the expression is equal 0, then 2 solutions
    else if (((b * b) - (4 * a * c)) == 0)
        cout << "1 solution";

    // Else no solutions
    else
        cout << "No solutions";
}

int main()
{
    int a = 2, b = 5, c = 2;
    checkSolution(a, b, c);
    return 0;
}

// Java Program to find the solutions of specified equations
public class GFG {

    // Method to check for solutions of equations
    static void checkSolution(int a, int b, int c)
    {

        // If the expression is greater than 0, 
        // then 2 solutions
        if (((b * b) - (4 * a * c)) > 0)
            System.out.println("2 solutions");

        // If the expression is equal 0, then 2 solutions
        else if (((b * b) - (4 * a * c)) == 0)
            System.out.println("1 solution");

        // Else no solutions
        else
            System.out.println("No solutions");
    }

    // Driver Code
    public static void main(String[] args)
    {
        int a = 2, b = 5, c = 2;
        checkSolution(a, b, c);
    }
}

# Python3 Program to find the 
# solutions of specified equations 

# function to check for
# solutions of equations 
def checkSolution(a, b, c) :

    # If the expression is greater
    # than 0, then 2 solutions 
    if ((b * b) - (4 * a * c)) > 0 :
        print("2 solutions")

    # If the expression is equal 0, 
    # then 1 solutions
    elif ((b * b) - (4 * a * c)) == 0 :
        print("1 solution")

    # Else no solutions 
    else :
        print("No solutions")

# Driver code
if __name__ == "__main__" :

    a, b, c = 2, 5, 2
    checkSolution(a, b, c)

# This code is contributed
# by ANKITRAI1

// C# Program to find the solutions 
// of specified equations
using System;
class GFG 
{

// Method to check for solutions of equations
static void checkSolution(int a, int b, int c)
{

    // If the expression is greater 
    // than 0, then 2 solutions
    if (((b * b) - (4 * a * c)) > 0)
        Console.WriteLine("2 solutions");

    // If the expression is equal to 0,
    // then 2 solutions
    else if (((b * b) - (4 * a * c)) == 0)
        Console.WriteLine("1 solution");

    // Else no solutions
    else
        Console.WriteLine("No solutions");
}

// Driver Code
public static void Main()
{
    int a = 2, b = 5, c = 2;
    checkSolution(a, b, c);
}
}

// This code is contributed by inder_verma

<?php
// Program to find the solutions 
// of specified equations

// Method to check for solutions 
// of equations
function checkSolution($a, $b, $c)
{

    // If the expression is greater 
    // than 0, then 2 solutions
    if ((($b * $b) - (4 * $a * $c)) > 0)
        echo "2 solutions";

    // If the expression is equal 0, 
    // then 2 solutions
    else if ((($b * $b) - 
              (4 * $a * $c)) == 0)
        echo "1 solution";

    // Else no solutions
    else
        echo"No solutions";
}

// Driver Code
$a = 2; $b = 5; $c = 2;
checkSolution($a, $b, $c);

// This code is contributed 
// by inder_verma
?>

<script>

// Javascript Program to find the solutions
// of specified equations

// Method to check for solutions of equations
function checkSolution(a, b, c)
{
    
    // If the expression is greater than 0, 
    // then 2 solutions
    if (((b * b) - (4 * a * c)) > 0)
        document.write("2 solutions");

    // If the expression is equal 0, then 2 solutions
    else if (((b * b) - (4 * a * c)) == 0)
        document.write("1 solution");

    // Else no solutions
    else
        document.write("No solutions");
}

// Driver Code
var a = 2, b = 5, c = 2;

checkSolution(a, b, c);

// This code is contributed by Ankita saini

</script>

Output: 

2 solutions

Time Complexity: O(1)

Auxiliary Space: O(1)