any concrete relationship between roots of polynomial and coeefficients+special pattern
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
101313
Minimal polynomial, determinants and invertibility
103246
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
71572
factor-square property (FSP) of polynomials
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
41193
Number of integral roots of a polynomial
143466
Roots of functions / polynomials
84400
Build a Companion Matrix of a Polynomial?
65661
Decomposition of a homogeneous polynomial
48977
Polynomials having as roots the sum (respectively, the product) of two algebraic elements
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
76482
Closure of the set of degree $n$ polynomials with $n$ real roots
81669
The logic of the AC Method of factoring quadratic polynomials
82262
minimal polynomial of nth root of 2 over $\mathbb Q$
1060
Minimal polynomial of intermediate extensions under Galois extensions.
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