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If p(x)=(1+x^2+x^4++x)/(1+x+x^2++x^(n-1)...

If `p(x)=(1+x^2+x^4++x)/(1+x+x^2++x^(n-1)^(2n-2)` is a polynomial in `x ,then n` can be a. `5` b. `10` c. `20` d. `17`

A

5

B

10

C

20

D

17

Text Solution

Verified by Experts

The correct Answer is:
A, D
`p(x)=((1-x^(2n))/(1-x^(2)))((1-x)/(1-x^(n)))=(1+x^(n))/(1+x)`
As p(x) is a polynomial , x=-1 must be a zero of `1+x^(n)`, i.e., `1+(-1)^(n)=0`. So, n must be odd.
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