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If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|...

If `|(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+c)`
where a, b, c are all different, then the determinant
`|(1,1,1),((x-a)^(2),(x -b)^(2),(x -c)^(2)),((x -b) (x -c),(x -c) (x -a),(x -a) (x -b))|` vanishes when

A

a+b+c=0

B

`x=(1)/(3)`(a+b+c)

C

`x=(1)/(2)`(a+b+c)

D

x=a+b+c

Text Solution

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The correct Answer is:
B
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