Quadratic equation whose roots are K times the roots of given equation
Given three integers A, B, and C representing the coefficients of a quadratic equation Ax2 + Bx + C = 0 and a positive integer K, the task is to find the coefficients of the quadratic equation whose roots are K times the roots of the given equation.
Examples:
Input: A = 1, B = 2, C = 1, K = 2
Output: 1 4 4
Explanation:
The given quadratic equation x2 + 2x + 1 = 0.
Roots of the above equation are -1, -1.
Double of these roots are -2, -2.
Therefore, the quadratic equation with the roots (-2, -2) is x2 + 4x + 4 = 0.
Input: A = 1, B = -7, C = 12, K = 2
Output: 1 -14 48
Approach: The given problem can be solved by using the concept of quadratic roots. Follow the steps below to solve the problem:
- Let the roots of the equation Ax2 + Bx + C = 0 be P and Q respectively.
- Then, the product of the roots of the above equation is given by P * Q = C / A and the sum of the roots of the above equation is given by P + Q = -B / A.
- Therefore, the product of the roots of the required equation is equal to:
(K * P ) * (K * Q) = K2 * P * Q = (K2 * C ) / A
- Similarly, the sum of the roots of the required equation is 2 * K (-B / C).
- Therefore, the required quadratic equation is equal to:
x2 – (Sum of the roots)x + (Product of the roots) = 0
=> Ax2 + (KB)x + (K2)C = 0
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
void findEquation( int A, int B, int C,
int K)
{
cout << A << " " << K * B
<< " " << K * K * C;
}
int main()
{
int A = 1, B = 2, C = 1, K = 2;
findEquation(A, B, C, K);
return 0;
}
|
Java
import java.util.*;
class GFG{
static void findEquation( int A, int B,
int C, int K)
{
System.out.print(A + " " + K * B +
" " + K * K * C);
}
public static void main(String []args)
{
int A = 1 , B = 2 , C = 1 , K = 2 ;
findEquation(A, B, C, K);
}
}
|
Python3
def findEquation(A, B, C, K):
print (A, K * B, K * K * C)
if __name__ = = '__main__' :
A, B, C, K = 1 , 2 , 1 , 2
findEquation(A, B, C, K)
|
C#
using System;
class GFG{
static void findEquation( int A, int B,
int C, int K)
{
Console.Write(A + " " + K * B +
" " + K * K * C);
}
public static void Main()
{
int A = 1, B = 2, C = 1, K = 2;
findEquation(A, B, C, K);
}
}
|
Javascript
<script>
function findEquation(A, B, C, K)
{
document.write( A + " " + K * B
+ " " + K * K * C);
}
var A = 1, B = 2, C = 1, K = 2;
findEquation(A, B, C, K);
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
Last Updated :
13 May, 2021
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