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