# Questions tagged [cubics]

This tag is for questions relating to cubic equations, these are polynomials with $~3^{rd}~$ power terms as the highest order terms.

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### Collinearity of the three roots of a cubic equation in the complex plane

The three roots of the equation $x^3+bx+c=0\;(b,c\in\Bbb C,c\ne0)$ in the complex plane are collinear iff$$k\in\Bbb R\land k\le-\frac{27}4$$where $k=\frac{b^3}{c^2}$. Original post on Math ...
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### Solving the system $x^3+y= 3x+4$, $2y^3+z = 6y+6$, $3z^3+x=9z+8$

Solve the system $$\begin{equation} \label{equation1} \begin{split} x^3+y= 3x+4 \\ 2y^3+z = 6y+6 \\ 3z^3+x=9z+8 \end{split} \end{equation}$$ By the theorem of triviality, I assumed $x=y=z=k$ and ...
### Prove that if $a+b\sqrt{2} + c\sqrt{4} = 0$ then $a=b=c=0$, where $a,b,c$ are rational numbers [duplicate]
Trying this for a while and, I found out that if there is another solution $(a_0,b_0,c_0)$, then there is an infinite amount of solutions $(a_0/2,b_0/2,c_0/2), (a_0/4,b_0/4,c_0/4) \ldots$, but I am ...