I'd like to be able to find the zeros of something like this:
$$0= k + \left[\binom{n}{2}-\binom{n}{1}\right]x+\left[\binom{n}{3}-\binom{n}{2}\right]x^{2}+\cdots+\left[\binom{n}{n}-\binom{n}{n-1}\right]x^n$$
Where $k$ and $n$ are general constants. What approach would you use?
Edit: I'm primarily interested in finding roots that are bound between 0 and 1, non-inclusive.
Hint :
$$(1+x)^n = 1+ \binom n1 x +\binom n2 x^2+...+\binom nn x^n $$