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if |{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(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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