Question:

If all roots of $z^3+az^2+bz+c=0$ are of unit modulus, then

(A) $|a|\leq3$

(B) $|b|\leq3$

(D) All of these

Step-by-Step Solution

Key Concept: Roots $z_1,z_2,z_3$ with $|z_i|=1$. $|a|=|z_1+z_2+z_3|\leq3$; $|b|=|z_1z_2+z_2z_3+z_3z_1|\leq3$; $|c|=|z_1z_2z_3|=1$.

All of (A),(B),(C) are true.

Correct Answer: (D) All of these