If $f(x)$ is a function with all coefficients $1$ or $-1$ and all roots real then degree of $f(x)$ can be
69523
Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
96620
Condition on degrees for existence of a tree
147325
Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
6722
to show $f$ is a polynomial in $z$
61640
Prove c exists for f:[0,1] -> R
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
48260
If $R=K[X]/(X^n)$, can represent any element as polynomial with degree $<n$
111569
Property of a polynomial with no positive real roots
92537
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
81758
Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero.
119999
A property of every real polynomial.
13981
Proof that every polynomial of odd degree has one real root
7567
Degree of Field Extensions and $F(\alpha)$