Find the value of the determinant `|[0,b^2a,c^2a],[a^2b,0,c^2b],[a^2c,b^2c,0]|`

If a^2+b^2+c^2+ab+bc+ca<=0 AA a, b, c in R then find the value of the determinant |[(a+b+2)^2, a^2+b^2, 1] , [1, (b+c+2)^2, b^2+c^2] , [c^2+a^2, 1, (c+a+2)^2]| : (A) abc(a^2 + b^2 +c^2) (B) 0 (C) a^3+b^3+c^3 + 3abc (D) 65

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

The value of the determinant ,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]| is

" 0.The value of the determinant "|[1,x,x^(2)],[1,b,b^(2)],[1,c,c^(2)]|" is: "

If a, b, c are the roots of the equation x^3-12x^2+39x-21=0 then find the value of the determinant |[a, b-c, c+b] , [ a+c, b, c-a] , [a-b, b+a, c]|

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

If a^2+b^2+c^2+a b+b c+c alt=0AAa ,b ,c in R , then value of the determinant |(a+b+2)^2a^2+b^2 1 1(b+c+2)^2b^2+c^2c^2+a^2 1(c+a+2)^2|e q u a l s 65 (b) a^2+b^2+c^2+31 4(a^2+b^2+c^2 (d) 0

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]|. The other factor in the value of the determinant is