To find root of $x^n+1=0$
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$
2519
Finding double root. An easier way?
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
90043
Show that if $r$ is an nth root of $1$ and $r\ne1$, then $1 + r + r^2 + ... + r^{n-1} = 0$.
38568
Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
91496
If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$
42916
Find the number of real roots of $1+x/1!+x^2/2!+x^3/3! + \ldots + x^6/6! =0$.
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
7463
Square root of a square
16660
Prove that any positive number has an $n$th root
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
47949
If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
148535
Finding the "triangular root" of a number.
148983
If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$
135178
Finding a quadratic equation from roots (Vieta's formula)
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
64448
Find a quadratic equation with root $x_1^2$ and $x_2^2$