Find the value of `|[a,a^(2),a^(3)],[b,b^(2),b^(3)],[c,c^(2),c^(3)]|`.

Find the value of: |[1 a^2 a^3],[1 b^2 b^3],[1 c^2 c^3]|

FInd x when det[[x+a,a^(2),a^(3)x+b,b^(2),b^(3)x+c,c^(2),c^(3)]]=0 where a,b,c are distinct numbers and a!=b!=c

Find the value of |[3,1,2],[a,b,c],[a^(2),b^(2),c^(2)]| .

Suppose a,b,c, gt0 and |(a^(3)-1,a^(2),a),(b^(3)-1,b^(2),b),(c^(3)-1,c^(2),c)|=0 then least possible value of a+b+c is ____________

Find the value of a^(3)+b^(3)+c^(3)-3abc if a+b+c=5 and a^(2)+b^(2)+c^(2)=29

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

Factorize the following 3,a+b+c,a^(3)+b^(3)+c^(3)a+b+c,a^(2)+b^(2)+c^(2),a^(4)+b^(4)+c^(4)a^(2)+b^(2)+c^(2),a^(3)+b^(3)+c^(3),a^(5)+b^(5)+c^(5)]|