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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

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

B

`x=2/3(a+b+c)`

C

`x=a+b+c`

D

None of these

Text Solution

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The correct Answer is:
A
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