Given two integers S and M, the task is to find the coefficients of the quadratic equation such that the sum and the product of the roots are S and M respectively.
Examples:
Input: S = 5, M = 6
Output: 1 -5 6
Explanation:
For the quadratic equation x2 – 5x + 6 = 0. The root of the equation are 2 and 3. Therefore, the sum of roots is 2 + 3 = 5, and the product of roots is 2*3 = 6.Input: S = -2, M = 1
Output: 1 2 1
Approach: The given problem can be solved by using the property of the Quadratic Equation as shown below:
For the above quadratic equation the roots are given by:
and
The sum of roots is given by:
=>
=>
=>
The product of roots is given by:
=>
=>
From the above two equations, if the value of a is 1 then the value of b is (-1)*S, and c is P. Therefore, the equation is given by:
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the quadratic // equation from the given sum and // products of roots void findEquation( int S, int M)
{ // Print the coefficients
cout << "1 " << (-1) * S << " "
<< M << endl;
} // Driver Code int main()
{ int S = 5, M = 6;
findEquation(S, M);
return 0;
} |
// Java program for the above approach import java.io.*;
class GFG{
// Function to find the quadratic // equation from the given sum and // products of roots public static void findEquation( int S, int M)
{ // Print the coefficients
System.out.println( "1 " + ((- 1 ) * S) + " " + M);
} // Driver code public static void main(String[] args)
{ int S = 5 , M = 6 ;
findEquation(S, M);
} } // This code is contributed by user_qa7r |
# Python3 program for the above approach # Function to find the quadratic # equation from the given sum and # products of roots def findEquation(S, M):
# Print the coefficients
print ( "1 " , (( - 1 ) * S), " " , M)
# Driver Code S = 5
M = 6
findEquation(S, M) # This code is contributed by Ankita saini |
// C# program for the above approach using System;
class GFG{
// Function to find the quadratic // equation from the given sum and // products of roots public static void findEquation( int S, int M)
{ // Print the coefficients
Console.Write( "1 " + ((-1) * S) + " " + M);
} // Driver code static void Main()
{ int S = 5, M = 6;
findEquation(S, M);
} } // This code is contributed by code_hunt |
<script> // Javascript program for the above approach // Function to find the quadratic // equation from the given sum and // products of roots function findEquation(S, M)
{ // Print the coefficients
document.write( "1 " + ((-1) * S) + " " + M);
} // Driver Code var S = 5, M = 6;
findEquation(S, M); // This code is contributed by Ankita saini </script> |
Output:
1 -5 6
Time Complexity: O(1)
Auxiliary Space: O(1)