Hello qtpipiFirst of all, let me write out what the question is asking. The first expression means:

And to say it has zeros means

And then, we are to derive a formula for

So, using the Remainder Theorem, are factors of .

Since there are of these factors, and is a polynomial of degree , this means that we can write as:

(This is what the expression means.)

Now the coefficient of is . So . And the coefficient of in the expansion of is which is . So:

So how do we find ?

Replace by :

which has zeros at

and

and, using the same method as before, the sum of the roots of this polynomial is

Grandad