Prove that all the roots of the equation $(1+z)^6+z^6=0$ are collinear.
109304
The roots of the equation $z^n=(1+z)^n$...
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
5410
Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
77820
Roots in a polynomial ring
13981
Proof that every polynomial of odd degree has one real root
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.
94682
Polynomial: prove there is no double root
92226
Prove $\sqrt6$ is irrational
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
52178
Prove the roots of $z^7+7z^4+4z+1=0$ lie inside a circle of radius $2$.
141371
Prove that $\alpha^n+\beta^n+\gamma^n \equiv 4^n+5^n+(-6)^n \pmod{17}$
86882
Proving Gauss' polynomial theorem (Rational Root Test)
66210
Prove that $z^n + 1/{z^n}$ is a rational number
100761
Find all $x$ such that $x^6 = (x+1)^6$.
131893
How to find the roots of $ x^4 + x + 1$ in the extension of $\Bbb F_2$?
140481
How to tell if a quartic equation has a multiple root.
40212
roots of $f(z)=z^4+8z^3+3z^2+8z+3=0$ in the right half plane