Sum of roots of a number
Is there a theorem related to the sum of the roots of a positive number?
For example, for any integer n=1,2,3.....N, and positive number , such that are the nth roots of , what is the sum of the roots,
In other words, is there a closed form, and general solution for the sum of roots, i.e.
Yes, it's , unless !
Hint : the sum of the roots of a polynomial is (up to sign) the coefficient of , and the roots of a complex number are the roots of .
So, are you saying the sum of the roots of is 0 for n not equal 1, and, for n=1, the sum must be simply ? Thanks.. looking at the , I guess that makes sense.. I had long since forgotten, if I ever even knew it, that the sum of roots equals coefficient of Z in the polynomial.
Comment for Bruno J
In general if we have a polynomial of degree in it can be written as...
... where the , are the roots of the polynomial. If the roots are all distinct then from (1) is easy to derive that is...
If with is...
Thanks! Do you have an idea what it's of? (Wink)
Originally Posted by wonderboy1953
Taking a stab.
Originally Posted by Bruno J.