Solving for the roots of high degree polynomials is quite challenging, I am wondering if there are any tricks that make it easier to solve for the roots of polynomials where most of the coefficients are zero, namely polynomials of the form
$x^n+bx^{n-1}+c$
Are there any theorems about roots of such polynomials, in terms of existence of real roots for example for conditions on $b$ and $c$. We know that the roots of
$x^n−1$ are given by $e^{2\pi}k/n$.
There also appears to be special formulas for the roots of
$x^n - x -c$
Given in the below paper http://arxiv.org/abs/math/9411224.