If `omega` is the cube root of unity, then what is one root of the equation `|{:(x^(2),-2x,-2omega^(2)),(2,omega,-omega),(0,omega,1):}|=0` ?

If omega is a cube root of unity, then 1+ omega^(2)= …..

If omega is cube root of unity, then a root of the equation |(x + 1,omega, omega^2),(omega, x + omega , 1),(omega^2 , 1, x + omega)| = 0 is

If omega is a complex cube root of unity, then a root of the equation |(x +1,omega,omega^(2)),(omega,x + omega^(2),1),(omega^(2),1,x + omega)| = 0 , is

If omega is a complex cube root of unity, then a root of the equation |(x +1,omega,omega^(2)),(omega,x + omega^(2),1),(omega^(2),1,x + omega)| = 0 , is

If omega is a cube root of unity, then omega + omega^(2)= …..

If omega is an imaginary cube root of unity, then a root of equation |(x+1,omega,omega^2),(omega,x+omega^2,1),(omega^2,1,x+2)|=0,can be

If omega is a complex cube root of unity then a root of the equation |[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]|=0 is

If 1,omega,omega^(2) are the cube roots of unity, then the roots of the equation (x-1)^(3)+8=0 are