Roots of polynomial with positive coefficients My question is very simple. Suppose we have a polynomial defined as follows:
$$p(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots+a_0 $$
where all of the $a_n$'s are all real and positive. Is there something that we can say about the roots of $p(x)$? Can we say the roots of $p(x)$ all contain negative real parts?
Thanks!

The simplest counter-example is $\;x^5+x^4+x^3+x^2+x+1$: its roots are 
$$\mathrm e^{\tfrac{\mathrm ik\pi}3},\quad k=1,\dots,5$$ 
and two of them have positive real parts.
Of course, this polynomial is not irreducible in $\mathbf Q[x]$.
