Prove that the following polynomial has no multiple roots
139305
Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.
152347
Proof that a certain entire function is a polynomial
7954
Roots of monic polynomial over a number ring
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
158063
A formula for the roots of a solvable polynomial
40014
A polynomial that is zero on an open set
116307
Polynomial whose only values are squares
53012
Irreducibility of a polynomial if it has no root (Capelli)
151729
Existence of a unique polynomial
69523
Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
133101
Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial
61548
What would be the roots of the derivative of this polynomial
21422
Multivariate polynomial with no mixed terms
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
41193
Number of integral roots of a polynomial
103763
Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$