The determinant `Delta(k)=|(a^2(a+b),a b,a c),(a b,b^2(a+k),b c),(a c,b c,c^2(1+k))|`is divisible by

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 determinant a^(2)(a+b),ab,acab,b^(2)(a+k),bcac,bc,c^(2)(1+k)]|

The determinant |a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a b| is divisible by- a. a+b+c b. (a+b)(b+c)(c+a) c. a^2+b^2+c^2 d. (a-b)(b-c)(c-a)

Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)| .

The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c, k^2+c^2, 1)| is (A) k(a+b)(b+c)(c+a) (B) k a b c(a^2+b^(2)+c^2) (C) k(a-b)(b-c)(c-a) (D) k(a+b-c)(b+c-a)(c+a-b)

If a,b,c are unequal then what is the condition that the value of the following determinant is zero Delta =|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|