Problem:

Let

be a polynomial of degree

with real coefficients

for

Show that if

for some

then

or

.

Ideas :

I'm kind of stuck on this one.

I observed that there are clearly no roots on the positive real axis. I could use Descarte's Rule of Signs if necessary.

I also know, via the same method described

here, that all roots have modulus less than or equal to 2.

I was thinking of writing

and using the statement that

to get some relationship between

and

using trig functions but it hasn't panned out for me so far.

I also wonder if Vieta's formula for the coefficients in terms of the roots might help.