Absolute difference between sum and product of roots of a quartic equation?

In this section we will see how to get the absolute difference between the sum of the roots and the products of the root of a quartic equation?

The quartic equation is like 𝑎𝑥⁴+𝑏𝑥³+𝑐𝑥²+𝑑𝑥+𝑒

We can solve the equation and then try to get the product and sum of the roots by some normal process, but that takes much time and that approach is not so efficient. In this kind of equation, we have two formulae. The Sum of roots are always −𝑏∕𝑎 and the product of roots are always 𝑒∕𝑎 . So we have to find only the value of ∣−𝑏∕𝑎− 𝑒∕𝑎∣ ∣

Algorithm

rootSumProdDiff(a, b, c, d, e)

begin
   sum := -b/a
   prod := e/a
   return |sum - prod|
end

Example

 Live Demo

#include<iostream>
#include<cmath>
using namespace std;
double rootSumProdDiff(double a, double b, double c, double d, double e){
   double sum = double(-b/a);
   double prod = double(e/a);
   return abs(sum - prod);
}
main() {
   double a,b,c,d,e;
   cout << "Enter a, b, c, d, e for equation ax^4 + bx^3 + cx^2 + dx + e:";
   cin >> a >> b >> c >> d >> e;
   cout << "Difference between sum and product of roots are: " << rootSumProdDiff(a, b, c, d, e);
}

Output

Enter a, b, c, d, e for equation ax^4 + bx^3 + cx^2 + dx + e:8 4 6 4 1
Difference between sum and product of roots are: 0.625