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I moved "monic" to the right place.
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Douglas Zare
Douglas Zare
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Say that a monic univariate polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of itsthe coefficients of $x^d,\ldots,x^1,x^0$ areis (strictly) positive.

For $f$ a monic univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?

Say that a monic univariate polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of its coefficients of $x^d,\ldots,x^1,x^0$ are (strictly) positive.

For $f$ a univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?

Say that a polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of the coefficients of $x^d,\ldots,x^1,x^0$ is (strictly) positive.

For $f$ a monic univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?

added 10 characters in body
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user2529
user2529

Say that a monic univariate polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of its coefficients of $x^d,\ldots,x^1,x^0$ are (strictly) positive.

For $f$ a univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?

Say that a univariate polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of its coefficients of $x^d,\ldots,x^1,x^0$ are (strictly) positive.

For $f$ a univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?

Say that a monic univariate polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of its coefficients of $x^d,\ldots,x^1,x^0$ are (strictly) positive.

For $f$ a univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?

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user2529
user2529

Stability of real polynomials with positive coefficients

Say that a univariate polynomial in an indeterminate $x$ with real coefficients of degree $d$ has positive coefficients if each of its coefficients of $x^d,\ldots,x^1,x^0$ are (strictly) positive.

For $f$ a univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?