The Eagle one is basically a Jackite fiberglass pole, 31ft long with a wire running up the middle of it.
Due to the length it is a 1/4 wave on 40 meters, which would make it a great antenna there, 1/2 on 20 meters, 3/4 wave on 15m and I guess a full wave or so on 10. Anything above 17m and you basically have high angle radiation. That being said I've used my 40m vertical on 15m and it works just swell there, and so so on ten, and that is after tuning it through 100ft of LMR400.
The best way to go with a antenna such as the Eagle one if you're going to use it on more than one band would be to put a auto tuner right at the base to take care of the matching. I guess secondly the next best thing would be to run some very low loss coax and a 4:1 unun, not a balun (like they say to do on the makers site).
I have one of these Jackite poles and last weekend for a demo set one up for my local clubs open house. I put a LDG- Z11 pro auto tuner right at the base, it happens to run on batteries, connected to the vertical itself through a 1:1 current choke and it worked fine with just two elevated radials. It worked on 15/17/20/30/40... and sort of worked on 80m. However on 80 I could not give it a fair test as this was during the day time and the only signals to be heard were local instate stuff, which is about the worst thing to use a vertical on 80m for. Signals on 20m were very strong.
If I were to ground mount the thing, I'd just put down as many radials as you can stand, maybe not all at once, but view it as a project over time. You should REALLY consider going the auto tuner route. You can use the battery powered LDG units, MFJ units that can be powered from DC through coax insertion, or of course the SGC units. Going with a UNUN or balun at the base and tuning in the shack would not be ideal, you would lose several DB. Running a 4:1 balun into the thing would be a terrible idea on 40m I would think, dropping impedance way down and causing a large loss probably.
Jackite fiberglass poles can be had on ebay for around 45-50 dollars shipped. Buy one and use the money saved to put towards a cheap auto tuner.
http://w9oy-sdr.blogspot.com/2009/09/43ft-vert.html there is a good read on remoting a in-shack tuner to the base of a antenna, happens to be a common MFJ auto tuner. The nice thing about MFJ tuners is one, you can power them through DC insertion into the coax, AND for about 40 bucks you can get remote control for them as well so you can manually adjust the tuner if you wish from the shack, that is SLICK and not many people know about it. It hooks up with standard serial cable which can be had for cheap as dirt.