Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
41193
Number of integral roots of a polynomial
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
61148
Finding real roots of $ P(x)=x^8 - x^7 +x^2 -x +15$
80502
$p(x)$ divided by $x-c$ has remainder $p(c)$? [Polynomial Remainder Theorem]
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
115834
Cubic polynomial with three (distinct) irrational roots
136310
Prime number in a polynomial expression
135385
$0 < a_0 \leq a_1 \leq \cdots \leq a_n$, 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 $|z| < 1$
114812
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
51019
Polynomial problem with two conditions
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
107765
Prove that there exists two roots in $[-1,1]$
145191
Content of a polynomial