Determinant



@kartikjha @AdvaitGirap open det and u will get
$a^3+b^3+c^33abc=0$ .
This can be factorised in d following ways:$(a+b+c)(a^2+b^2+c^2abbcca)=0$
Or
$(a+bw+cw^2)(a^2+b^2w^2+c^2wabwbc$
$caw^2$ $)=0$ Now try switching
$w$ in the second method.

@kartikjha correct option will be 4th

@harshalpatil yuss. Mentioned already 👍

@advaitgirap i wanted to mention dat it is not necessary dat a=b=c=1 for the other two conditions