ISRO 2007-ECE Roots of equation

Question

If a,b,c are the roots of equations $x^3$ + p$x^ 2$ +q$x$+p=0, Then the value of $$tan^{-1} a+ tan^{-1 }b+tan^{-1}c$$   is

a) n π /4

b) n π /2

c) n π

d) 2n π

Answer 1

From the given equation we get, a+b+c= -p and ab+bc+ca = q and abc= -p then