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Check if roots of a Quadratic Equation are numerically equal but opposite in sign or not

  • Last Updated : 23 Aug, 2021

Given the coefficients (constants) of a quadratic equation ax^{2} + bx + c=0    , i.e. a, b, and c; the task is to check whether roots of the equation represented by these constants are numerically equal but opposite in sign or not.
Examples: 
 

Input: a = 2, b = 0, c = -1 
Output: Yes 
Explanation: 
The given quadratic equation is 2x^{2}-2=0
Its roots are (1, -1) which are numerically equal but opposite in sign
Input: a = 1, b = -5, c = 6 
Output: No 
Explanation: 
The given quadratic equation is x^{2}-5x+6=0
Its roots are (2, 3) which are not numerically equal and opposite in sign 
 

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Approach: 
To check whether roots are numerically equal but opposite in sign or not: 
 

Quadratic Equation: ax^{2} + bx + c = 0
Let the roots be \alpha    and \beta
Sum of roots = \alpha + \beta    \frac{-b}{a}
Since roots are opposite in sign only, therefore \alpha = -\beta
Therefore, 
-\beta + \beta = \frac{-b}{a}
0 = \frac{-b}{a}
b = 0    , i.e, coefficient of x is 0. 
 

Hence we have to only check if b is 0 or not, for the roots to be numerically equal but opposite in sign.
Below is the implementation of the above approach:
 

C++




// C++ program to check if roots
// of a Quadratic Equation are
// numerically equal but opposite
// in sign or not
 
#include <iostream>
using namespace std;
 
// Function to find the required answer
void checkSolution(int a, int b, int c)
{
    if (b == 0)
        cout << "Yes";
    else
        cout << "No";
}
 
// Driver code
int main()
{
    int a = 2, b = 0, c = 2;
 
    checkSolution(a, b, c);
 
    return 0;
}


Java




// Java program to check if roots
// of a Quadratic Equation are
// numerically equal but opposite
// in sign or not
import java.util.*;
class GFG{
 
// Function to find the required answer
static void checkSolution(int a, int b, int c)
{
    if (b == 0)
        System.out.print("Yes");
    else
        System.out.print("No");
}
 
// Driver code
public static void main(String args[])
{
    int a = 2, b = 0, c = 2;
 
    checkSolution(a, b, c);
}
}
 
// This code is contributed by Akanksha_Rai


Python3




# Python3 program to check if roots
# of a quadratic equation are
# numerically equal but opposite
# in sign or not
 
# Function to find the required answer
def checkSolution(a, b, c):
 
    if b == 0:
        print("Yes")
    else:
        print("No")
 
# Driver code
a = 2
b = 0
c = 2
 
checkSolution(a, b, c)
     
# This code is contributed by divyamohan123


C#




// C# program to check if roots
// of a Quadratic Equation are
// numerically equal but opposite
// in sign or not
using System;
class GFG{
 
// Function to find the required answer
static void checkSolution(int a, int b, int c)
{
    if (b == 0)
        Console.Write("Yes");
    else
        Console.Write("No");
}
 
// Driver code
public static void Main()
{
    int a = 2, b = 0, c = 2;
 
    checkSolution(a, b, c);
}
}
 
// This code is contributed by Akanksha_Rai


Javascript




<script>
 
// Javascript program to check if roots
// of a Quadratic Equation are
// numerically equal but opposite
// in sign or not
 
// Function to find the required answer
function checkSolution(a, b, c)
{
    if (b == 0)
        document.write("Yes");
    else
        document.write("No");
}
 
// Driver code
a = 2, b = 0, c = 2;
checkSolution(a, b, c);
  
</script>


Output: 

Yes

 

Time Complexity: O(1)

Auxiliary Space: O(1)




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