Show that $f$ has no rational root.
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
111569
Property of a polynomial with no positive real roots
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
36862
A question about proving that there is no greatest common divisor
148310
Showing rational numbers are algebraic
75012
Additive group of rationals has no minimal generating set
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
125604
Proof that $\mathbb{Z}$ has no zero divisors
103246
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
141273
When is $\sin(x)$ rational?
127605
What are some methods to show $\log$ is not a rational function?