query: Polynomial $p(z)$ in $\mathbb{C}$ has no zero whose modulus does not exceed $1$
positive_passages.docid: 150689
positive_passages.text: All the zeroes of $p(z)$ lie inside the unit disk
negative_passages.docid: 155575
negative_passages.text: Proving a polynomial $f(x)$ composite for infinitely many $x$
negative_passages.docid: 96116
negative_passages.text: Show $P(z) $ is a polynomial of degree $n-1$ interpolating an Analytic function.
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
negative_passages.docid: 2408
negative_passages.text: Show that a polynomial has at least one positive solution/root.
negative_passages.docid: 157266
negative_passages.text: Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
negative_passages.docid: 42265
negative_passages.text: A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
negative_passages.docid: 115004
negative_passages.text: If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
negative_passages.docid: 120940
negative_passages.text: An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 21862
negative_passages.text: Proof of lack of pure prime producing polynomials.
negative_passages.docid: 137669
negative_passages.text: $P$ is a monic polynomial of degree $n$ , then which are correct?
negative_passages.docid: 135385
negative_passages.text: $0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $ p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$
negative_passages.docid: 64878
negative_passages.text: Is this polynomial irreducible in $\mathbb{Q}$?
negative_passages.docid: 82204
negative_passages.text: Prove $ \lim_{n\to\infty}\sqrt[n]{p(n)}=1 $ for polynomial
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 141078
negative_passages.text: Domain over which a polynomial is strictly positive