Given a quartic equation in the form 
, determine the absolute difference between the sum of its roots and the product of its roots. Note that roots need not be real – they can also be complex.
Examples:
Input: 4x^4 + 3x^3 + 2x^2 + x - 1 Output: 0.5 Input: x^4 + 4x^3 + 6x^2 + 4x + 1 Output: 5
Approach: Solving the quartic equation to obtain each individual root would be time-consuming and inefficient, and would require much effort and computational power. A more efficient solution utilises the following formulae:
The quarticalways has sum of roots
,and product of roots
.
always has sum of roots 
,and product of roots 
. Hence by computing 
we find the absolute difference between sum and product of roots.
Below is the implementation of above approach:
C++
// C++ implementation of above approach #include <bits/stdc++.h> using namespace std; // Function taking coefficient of // each term of equation as input double sumProductDifference(int a, int b, int c, int d, int e) { // Finding sum of roots double rootSum = (double)(-1 * b) / a; // Finding product of roots double rootProduct = (double) e / a; // Absolute difference return abs(rootSum - rootProduct); } // Driver code int main() { cout << sumProductDifference(8, 4, 6, 4, 1); return 0; } // This code is contributed // by ANKITRAI1 |
Java
// Java implementation of above approach public class GFG { // Function taking coefficient of // each term of equation as input static double sumProductDifference(int a, int b, int c, int d, int e) { // Finding sum of roots double rootSum = (double)(-1 * b) / a; // Finding product of roots double rootProduct = (double) e / a; // Absolute difference return Math.abs(rootSum - rootProduct); } // Driver Code public static void main(String args[]) { System.out.println(sumProductDifference(8, 4, 6, 4, 1)); }} |
Python3
# Python implementation of above approach# Function taking coefficient of # each term of equation as inputdef sumProductDifference(a, b, c, d, e): # Finding sum of roots rootSum = (-1 * b)/a # Finding product of roots rootProduct = e / a # Absolute difference return abs(rootSum-rootProduct) print(sumProductDifference(8, 4, 6, 4, 1)) |
C#
// C# implementation of above approach using System;class GFG{// Function taking coefficient of// each term of equation as inputstatic double sumProductDifference(int a, int b, int c, int d, int e) { // Finding sum of roots double rootSum = (double)(-1 * b) / a; // Finding product of roots double rootProduct = (double) e / a; // Absolute difference return Math.Abs(rootSum - rootProduct);}// Driver Codepublic static void Main() { Console.Write(sumProductDifference(8, 4, 6, 4, 1));}}// This code is contributed // by ChitraNayal |
PHP
<?php// PHP implementation of above approach // Function taking coefficient of // each term of equation as input function sumProductDifference($a, $b, $c, $d,$e) { // Finding sum of roots $rootSum = (double)(-1 * $b) / $a; // Finding product of roots $rootProduct = (double) $e / $a; // Absolute difference return abs($rootSum - $rootProduct); } // Driver code echo sumProductDifference(8, 4, 6, 4, 1); // This code is contributed // by Shivi_Aggarwal?> |
Javascript
<script>// Javascript implementation of above approach // Function taking coefficient of// each term of equation as inputfunction sumProductDifference(a, b, c, d, e) { // Finding sum of roots var rootSum = (-1 * b) / a; // Finding product of roots var rootProduct = e / a; // Absolute difference return Math.abs(rootSum - rootProduct);}// Driver Codedocument.write(sumProductDifference(8, 4, 6, 4, 1));// This code is contributed by Ankita saini</script> |
Output:
0.625
Time Complexity: O(1)
Auxiliary Space: O(1)
Explanation: The input equation is 
.
By finding 
, we get 
,
which is 
, or 
.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
