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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

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

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

Zeros of polynomials with real positive coefficients,

and a proof can be found here: http://www.math.purdue.edu/~eremenko/dvi/saddle10.pdf

@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.

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

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

Zeros of polynomials with real positive coefficients,

and a proof can be found here: http://www.math.purdue.edu/~eremenko/dvi/saddle10.pdf

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

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

Zeros of polynomials with real positive coefficients,

and a proof can be found here: http://www.math.purdue.edu/~eremenko/dvi/saddle10.pdf

@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.