Yes. This is a part of my answer to another MO question,

https://mathoverflow.net/questions/134998/zeros-of-polynomials-with-real-positive-coefficients,

@David Handelman: thanks for the reference! I will insert it to my paper.

EDIT. In fact, Theorem 1 in the preprint cited above is not new. This was found as a
result of David's answer. The revised preprint is posted on the arxiv and here
http://www.math.purdue.edu/~eremenko/dvi/saddle13.pdf