Given $p(x)$ is a polynomial with integer coefficients and that $p(a)=1$ for some integer $a$ prove that $p(x)$ has no more than two integral roots.
35478
Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
13083
If for a polynomial $P(k) = 2^k$ for $k = 0, 1, . . . , n$, what is $P(n+1)$?
47792
Integer coefficient polynomial - values as powers of 2
92701
let $a,b,c \in\mathbb{R} ,a<3$ and all roots $p(x)=x^3+ax^2+bx+c=0$ be negative . then prove that $b+c\neq 4$
112334
Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
69523
Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
134068
When polynomials f(x) and f'(x) are relatively prime, f(x) has no repeated roots. Why?
119991
Why Rational Root Theorem requires integer coefficient polynomials?
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
41193
Number of integral roots of a polynomial
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
2408
Show that a polynomial has at least one positive solution/root.
145191
Content of a polynomial
155559
Quickest way to determine a polynomial with positive integer coefficients
65459
Roots of polynomials in field of prime characteristic p