$ x^{3}-x+a=0 $ and a is an uneven integer, show the polynomial has no rational root (Q)
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
139305
Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
77820
Roots in a polynomial ring
142642
$A=\begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, $X^2=A$ has no solutions
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
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 $|z| < 1$
89677
Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$?
99000
No polynomial with integer coefficients satisfies the conditions
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
115834
Cubic polynomial with three (distinct) irrational roots
141093
How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
80002
zeros of a polynomial
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
21972
How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?