Show that a complex polynomial of degree $n$ doesn't have zeros in a unit ball
96592
Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
118085
complex polynomial satisfying inequality
76482
Closure of the set of degree $n$ polynomials with $n$ real roots
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
4192
Non-algebraically closed field in which every polynomial of degree $<n$ has a root
76955
Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros
2408
Show that a polynomial has at least one positive solution/root.
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
40014
A polynomial that is zero on an open set
91388
Prove that $f$ is a polynomial if one of the coefficients in its Taylor expansion is 0
152982
Show that the range of $p(z)e^{q(z)}$ for nonconstant polynomials $p$ and $q$ is all of $\mathbb{C}$.
134726
Show the polynomial is irreducible in $\textbf Z_2$
150689
All the zeroes of $p(z)$ lie inside the unit disk
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros