Question

1+x+x^2+x^3=0 then 1+x+x^2+x^3...x^2008=

Answer 1

$1 + x + x {}^{2} + x {}^{3} = 0........(i)$
Therefore.....
$1 + x + x {}^{2} + x {}^{3} ..... + x {}^{2008} = 0$
Because in equation (i) x turns out to be 0 or -1 as the total is 0
The last root value of x is 2008 which is even and hence answer is 0
If it would have been odd then answer would be -1
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