`Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)|` is divisible by `a+b` b. `a+2b` c. `2a+3b` d. `a^2`

Let Delta=|(a,a^(2),0),(1,2a+b,(a+b)^(2)),(0,1,2a+3b)| then

Let f(a,b)=|{:(a,a^2,0),(1,(2a+b),(a+b)^2),(0,1,(2a+3b)):}| , then

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

If a!=b!=c\ a n d\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 then a+b+c=0 b. a b+b c+c a=0 c. a^2+b^2+c^2=a b+b c+c a d. a b c=0

a, b are the real roots of x2+ px +1-0 and c, d are the real roots of 2 x + qx + 1 = 0 then (a-c)(h-c)(a + d)(b + d) is divisible by n) a+b+c+d (b) a +b-c-d (d) a -b-c-d (c) a-b+c-d

If (a-1)^(2)+(b+2)^(2)+(c+1)^(2)=0 then 2a-3b+7c is

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

If [[a,a^(2),a^(3)-1b,b^(2),b^(3)-1c,c^(2),c^(3)-1]]=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