I need to calculate the minimum value of the following poynomial:
where is even and .
I can transform this polynomial into
by the means of Vieta's formula (PlanetMath: Vieta's formula) but this time it will not be easy to find the roots of .
I really wonder if this is something well-known.
Thanks for the help again.
Note: It also helps me to find good upper and lower bounds for .