i think u have to expand it, arrange in increasing order of coefficients. let it be

 f(x) no of changes in sign as u move from left to right gives  no of positive  roots.

 

substitite -x ie  f(-x). no of change in sign: no of -ve real roots

 

3- sum of above. is no of imaginary roots.

 

for ur question

3x³ - x ²(3a - 3b - 3c) + x 3( a² + b² + c ²) - (a³ + b ³ + c³)=0

( constant do not matter. don't contribute to sign)

no of + roots: 3

- ve : 0

im= 3-3 =0.

 

ans: 3 real roots no imaginary roots.

rate me if i am i correct????