Prove that the zeros of the polynomial $P(z)=z^7+7z^4+4z+1$ lie inside the disk of radius $2$ centered at the origin.
52178
Prove the roots of $z^7+7z^4+4z+1=0$ lie inside a circle of radius $2$.
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
134726
Show the polynomial is irreducible in $\textbf Z_2$
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
91388
Prove that $f$ is a polynomial if one of the coefficients in its Taylor expansion is 0
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
54212
Another polynomial equation
96592
Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
133101
Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial
101824
Proving zeros inside a disk using Maximum Principle?
100862
Polynomials with rational zeros
122686
Find the root of the polynomial?
81063
If $p$ is a polynomial, then either $\,p(z)=z^n\,$ or $\,\max_{|z|=1}|p(z)|>1$.
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
31544
How to prove that this polynomial is larger than another for positive reals?
6722
to show $f$ is a polynomial in $z$
131881
Show that the roots of P' lie in the same half plane as the roots of P