Easy and elementary proof that roots of a polynomial cannot contain a ball
40014
A polynomial that is zero on an open set
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
103932
How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?
82771
Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded
73454
Prove that $f$ has finite number of roots
118817
Polynomials in nature
143321
Number of roots of a polynomial over a finite field
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
148451
Polynomial inequality proof
14447
Direct proof that $\pi$ is not constructible
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
154507
If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
15914
Prove that any polynomial function is continuous
99737
Using Rouché's theorem to find a compact domain for the roots of a polynomial
158063
A formula for the roots of a solvable polynomial
122050
Algebraic extension of perfect field in which every polynomial has a root is algebraically closed