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

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

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, therfore \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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

Yes

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