$p(x) \in T[x]$. For $\alpha \in T$ to be a multiple root of $p(x)$, a necessary and sufficient condition is that $p(\alpha)=0$ and $p'(\alpha)=0$
45811
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.
135385
$0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $ p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$
115533
Inequality for small values of $t$
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
31898
Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
72920
$x \perp y$ if and only if $\Vert x + \alpha y \Vert \ge \Vert x \Vert$ for all scalars $\alpha$
135941
Derivative of $|x|^\alpha$
57639
Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
134068
When polynomials f(x) and f'(x) are relatively prime, f(x) has no repeated roots. Why?
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
145094
Is my basis for $U=\{p \in \mathcal P_4(\mathbb R) \mid p(6)=0\}$ correct?
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
27278
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 $\alpha -1$.
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial