Generate Quadratic Equation having given sum and product of roots
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++
#include <bits/stdc++.h>
using namespace std;
void findEquation( int S, int M)
{
cout << "1 " << (-1) * S << " "
<< M << endl;
}
int main()
{
int S = 5, M = 6;
findEquation(S, M);
return 0;
}
|
Java
import java.io.*;
class GFG{
public static void findEquation( int S, int M)
{
System.out.println( "1 " + ((- 1 ) * S) + " " + M);
}
public static void main(String[] args)
{
int S = 5 , M = 6 ;
findEquation(S, M);
}
}
|
Python3
def findEquation(S, M):
print ( "1 " , (( - 1 ) * S), " " , M)
S = 5
M = 6
findEquation(S, M)
|
C#
using System;
class GFG{
public static void findEquation( int S, int M)
{
Console.Write( "1 " + ((-1) * S) + " " + M);
}
static void Main()
{
int S = 5, M = 6;
findEquation(S, M);
}
}
|
Javascript
<script>
function findEquation(S, M)
{
document.write( "1 " + ((-1) * S) + " " + M);
}
var S = 5, M = 6;
findEquation(S, M);
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
Last Updated :
04 May, 2021
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