Dear all,

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 .