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Homework Statement
Find all ##a,b,c\in\mathbb{R}## for which the zeros of the polynomial ##az^3+z^2+bz+c=0## are in this relation $$z_1^3+z_2^3+z_3^3=3z_1z_2z_3$$
Homework Equations
we know that if we have a polynomial of degree 3 the zeroes have relation in this case
##z_1+z_2+z_3=1/a##
##z_1z_2+z_1z_3+z_2z_3=b/a ##
##z_1z_2z_3=c/a##
The Attempt at a Solution
I've tried doing something with the vietto rules but I have not really gotten anything. Any tip on how to even start the problem would be really appreciated
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