Odd-degree polynomials have roots (Intermediate Value Theorem)
13981
Proof that every polynomial of odd degree has one real root
69575
If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.
139420
How do I use the Intermediate Value Theorem in this question?
156034
sufficient condition for a polynomial to have roots in $[0,1]$
40502
The Degree of Zero Polynomial.
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
86882
Proving Gauss' polynomial theorem (Rational Root Test)
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
135774
Alternating roots of $f(x) = \exp(x) \sin(x) -1$ and $\exp(x)\cos(x) +1$
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
60816
Irreducibility of special cyclotomic polynomial.
158063
A formula for the roots of a solvable polynomial
70249
Irreducibility of Polynomials in $k[x,y]$
152347
Proof that a certain entire function is a polynomial
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
77820
Roots in a polynomial ring