query: Use $\alpha, \beta, \gamma $ roots of a polynomial to construct another polynomial
positive_passages.docid: 27278
positive_passages.text: Let $\alpha \in \overline{\Bbb Q}$ a root of $X^3+X+1\in\Bbb Q[X]$. Calculate the minimum polynomial of $\alpha^{-1}$ en $\alpha -1$.
negative_passages.docid: 41028
negative_passages.text: Is there a combinatorial way to see the link between the beta and gamma functions?
negative_passages.docid: 41193
negative_passages.text: Number of integral roots of a polynomial
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 99835
negative_passages.text: Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 97454
negative_passages.text: Find the value of $\alpha-\beta$ if $g(x,y)=\alpha x+\beta y$ is a Hahn-Banach extension of $f$
negative_passages.docid: 39082
negative_passages.text: Proving $x^\alpha-\alpha x \le 1- \alpha $
negative_passages.docid: 155559
negative_passages.text: Quickest way to determine a polynomial with positive integer coefficients
negative_passages.docid: 155245
negative_passages.text: root of an odd degree polynomial
negative_passages.docid: 48977
negative_passages.text: Polynomials having as roots the sum (respectively, the product) of two algebraic elements
negative_passages.docid: 84400
negative_passages.text: Build a Companion Matrix of a Polynomial?
negative_passages.docid: 126940
negative_passages.text: Converting expressions to polynomial form
negative_passages.docid: 116795
negative_passages.text: Easiest way to extract the coefficient of a polynomial
negative_passages.docid: 93123
negative_passages.text: Systems of linear equations to calculate $\alpha$ and $\beta$
negative_passages.docid: 72410
negative_passages.text: If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$