# Homework Help: Poly function of degree n with no roots

1. Dec 23, 2009

### Dafe

1. The problem statement, all variables and given/known data

(a) If n is even find a polynomial function of degree n with n roots.
(b) If n is odd find one with only one root.

2. Relevant equations
N/A

3. The attempt at a solution

If by no roots, they mean no real roots then I guess:
$$f(x) = x^n+1$$ would work for both even and odd n's.
The roots would be i and -i if n is even, and -1, and two complex roots if it's odd..

Suggestions are very welcome :)

2. Dec 23, 2009

### HallsofIvy

Yes, that looks to me to be a perfectly good answer. However, "The roots would be i and -i if n is even, and -1, and two complex roots if it's odd" is true only for n= 2 and 3. For general n, if n is even, then all n roots are non-real, i and -i being two of the. If n is odd, -1 is a root and the other n-1 roots are non-real.

3. Dec 23, 2009

### Dafe

Ah, I should have stated that, thank you.
You are usually the one that answers all questions I post around here. It's incredible that you do that for free..You should set up a paypal account :)
Thanks again.