If a+b+c=0, then one of the solutions of vmatrix a-x&c&b &b-x&a &a&c-x vmatrix =0 is

NDA 2018 Mathematics question

If , then one of the solutions of is

(A)
(B) (this is also correct)
(C)
(D)Correct

Answer: (D)

Solution

Add all the columns to the first: each entry of the first column becomes , so is a factor and is a solution. Taking out and expanding the remaining determinant gives $ =

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Question ID VK-028950