query: Is there a polynomial whose Coefficients in $\mathbb Q$ such that none of roots of this polynomial be in the root closure of $\mathbb Q$?
positive_passages.docid: 155962
positive_passages.text: Are there irreducible polynomials that are partially solvable by radicals?
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 76640
negative_passages.text: Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
negative_passages.docid: 53432
negative_passages.text: What is the algebraic closure of $\mathbb F_q$?
negative_passages.docid: 99000
negative_passages.text: No polynomial with integer coefficients satisfies the conditions
negative_passages.docid: 121658
negative_passages.text: $x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
negative_passages.docid: 99835
negative_passages.text: Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
negative_passages.docid: 146591
negative_passages.text: Inseparable polynomial over a non-perfect field
negative_passages.docid: 85586
negative_passages.text: Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
negative_passages.docid: 4885
negative_passages.text: Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$
negative_passages.docid: 107281
negative_passages.text: Proof of Existence of Algebraic Closure: Too simple to be true?
negative_passages.docid: 64878
negative_passages.text: Is this polynomial irreducible in $\mathbb{Q}$?
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 19511
negative_passages.text: Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
negative_passages.docid: 67001
negative_passages.text: Factorizing polynomials over fields other than $\mathbb{C}$
negative_passages.docid: 106914
negative_passages.text: Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree