Question

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`

Answer 1

Correct Answer - 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`