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If f(x)=|1x x+1 2x x(x-1)(x+1) x3 x(x-1)...

If f(x)=`|1x x+1 2x x(x-1)(x+1) x3 x(x-1) x(x-1)(x-2) (x+1)x(x-1)|` then f(500) is equal to 0 b. 1 c. 500 d. -500

A

0

B

1

C

100

D

-100

Text Solution

Verified by Experts

Given,
`f(x) = |{:(" "1 , " "x, " "x+1),(" "2x, " "x(x-1), " "(x+1)x),(3x(x-1), x(x-1)(x-2), (x+1)x(x-1)):}|`
Applying `C_(3) to C_(3) -(C_(1) + C_(2))`
`=|{:(" "1 , " "x, 0),(" "2x, " "x(x-1), 0),(3x(x-1), x(x-1)(x-2), 0):}|= 0`
`therefore f(x) = 0 rArr f(100) = 0`
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