Check if roots of a Quadratic Equation are numerically equal but opposite in sign or not
Given the coefficients (constants) of a quadratic equation , 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
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
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:
Let the roots be and
Sum of roots = =
Since roots are opposite in sign only, therefore
Therefore,
, 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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