MathRevolution wrote:
[GMAT math practice question]
Suppose \(x=-1\) and \(k\) is a positive number. If \(n\) is a positive root of the equation \(n^4 – 2^{4k} = 0\), what is the value of \(x+x^n+x^{n+1}+x^{n+2}\)?
A. \(-2\)
B. \(-1\)
C. \(0\)
D. \(1\)
E. \(2\)
\(n^4-2^{4k}=0=>n^4=2^{4k}\). Taking fourth root of both sides we have
\(n=2^k=Even\) as \(k\) is a positive integer(Note as \(n\) is a positive root, so \(n=-2^k\) is not possible here)
Hence \(x+x^n+x^{n+1}+x^{n+2}=-1+(-1)^{even}+(-1)^{odd}+(-1)^{even}=0\)
Option
C