If `3x^(2)-2ax+(a^(2)+2b^(2)+2c^(2))=2(ab+bc)`, then `a`, `b`, `c` can be in

(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

|(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

If a+b+c=4 and a^(2)+b^(2)+c^(2)+3(ab+bc+ac)=21 where a, b, c in R then ab+bc+ca=

If quadratic equation ax^(2) + bx + ab + bc + ca - a^(2) - b^(2) - c^(2) = 0 where a, b, c distinct reals, has imaginary roots than (A) a+b+ab+bc+calta^(2)+b^(2)+c^(2) (B) a-b+ab+bc+cagta^(2)+b^(2)+c^(2) (C) 4a+2b+ab+bc+calta^(2)+b^(2)+c^(2) (D) 2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0

If quadratic equation ax^(2) + bx + ab + bc + ca - a^(2) - b^(2) - c^(2) = 0 where a, b, c distinct reals, has imaginary roots than (A) a+b+ab+bc+calta^(2)+b^(2)+c^(2) (B) a-b+ab+bc+cagta^(2)+b^(2)+c^(2) (C) 4a+2b+ab+bc+calta^(2)+b^(2)+c^(2) (D) 2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0

If c^(2) ne ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)=0 are equal, then show that a^(3)+b^(3)+c^(3)=3abc" or "a=0

Let a, b and c are the roots of the equation x^(3)-7x^(2)+9x-13=0 and A and B are two matrices given by A=[(a,b,c),(b,c,a),(c,a,b)] and B=[(bc-a^(2),ca-b^(2),ab-c^(2)),(ca-b^(2),ab-c^(2),bc-a^(2)),(ab-c^(2),bc-a^(2),ca-b^(2))] , then the value |A||B| is equal to

Let a, b and c are the roots of the equation x^(3)-7x^(2)+9x-13=0 and A and B are two matrices given by A=[(a,b,c),(b,c,a),(c,a,b)] and B=[(bc-a^(2),ca-b^(2),ab-c^(2)),(ca-b^(2),ab-c^(2),bc-a^(2)),(ab-c^(2),bc-a^(2),ca-b^(2))] , then the value |A||B| is equal to