Roots of cubic polynomial lying inside the circle Show that all roots of $a+bz+cz^2+z^3=0$ lie inside the circle
$|z|=max{\{1,|a|+|b|+|c| \}}$
Now this problem is given in Beardon's Algebra and Geometry third chapter on complex numbers. 
What might be relevant for this problem: 


*

*author previously discussed roots of unity;

*a little (I mean abut a page of informal discussion) about cubic and quartic equations; 

*then gave proof of fundamental theorem of algebra (the existence of root was given as a informal proof and rest using induction) and then the corollary of it (If $p(z) = q(z)$
at $n + 1$ distinct points then $p(z) = q(z)$ for all $z$, where both polynomials are of degree at most $n$);


I was trying to see how I should approach it with no success for quite some time. Looked on the net and found, that this would be kind of easy with Rouche's theorem, but I was not given that. So is it possible to solve it in a simple way with what was given? Thanks!

I'd simply be looking at showing that the $z^3$ term was dominant, so there could be no roots beyond the bound. I don't think it is at all sophisticated.
