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Find the sum of the roots (real or complex) of the equation `x^2001 + (1/2-x)^2001=0` . (a) `2000` (b) `2001` (c) `1000` (d) `500`

A

`2000`

B

`2001`

C

`1000`

D

`500`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `x^(2001)-["^(2001)C_(0)x^(2001)-^(2001)C_(1)x^(2000)*(1)/(2)+^(2001)C_(2)x^(1999)*(1)/(4)...]=0`
`:. ^(2001)C_(1)x^(2000)*(1)/(2)-^(2001)C_(2)x^(1999)*(1)/(4)...=0`
sum of the roots `=^(2001)C_(2)*(1)/(4)*(2)/("^(2000)C_(1))=(2001*2000)/(4*2001)=500`
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