find maximum and minimum value of $|z|$ If $a,b,c$ are complex number of equal magnitude and satisfy $az^2+bz+c=0,$ 
then finding maximum and minimum value of $|z|$
with the help of triangle inequality $|az^2+bz+c|\leq |az^2|+|bz|+|c|=|a||z|^2+|b||z|+|c|$
now let $|a|=|b| = |c| = k>0$
so $|az^2+bz+c|\leq k(|z|^2+|z|+1)$
so $|z|^2+|z|+1\geq 0$
wan,t be able to go after that, help me

We can divide across by $a$ and get $z^2+bz+c= 0$ with $|b|=|c| = 1$. Solving
the quadratic gives
$z = {1 \over 2} (-b \pm \sqrt{b^2 -4c} ) $. From this we get
$\sqrt{5}-1 \le 2 |z| \le \sqrt{5}+1$, and by choosing $b=1,c=-1$ we see
that these bounds are attained.
