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Feedpoint impedance on 20 will be in the thousands of ohms. You can force things with a "tuner" (actually, you'll HAVE to use some sort of matching network). Why not build a 40 meter dipole and a separate 20 meter dipole?

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If you're like everybody else,
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73 de K7KBN

Huh... why didn't I think of that. You stole my idea Beetle, shame on you.
- 'Doc

Dang, while we're at it, why not add on a 10/11 meter?

KC9PYV, You realize that you can you can do this with just one feedline, right?

That would be a fan dipole? I never really looked at an exact plan for one. I think I will be building a couple of antennas in the near future, but for now I'm going to give the one I have a try. I'm just waiting on my feedline to come in the mail.

Why don't you make a fan dipole using coax, that would solve the ladder line problem. you just cut one dipole for 40m and one for 20m and connect them to a center connector, this way the 40m could be in a sort of V configuration on one side of the roof and the 20m same way on the other side and the coax should give you minimal lose. shouldn't be hard to make and cheap.

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If you have a couple bucks and only intend on running 100W, a wide range auto tuner feeding a loop would work pretty well for you.

SGC-237, stuck in a Tupperware bin, tucked up under an eave as the tuner, then run wooden poles just a few feet off the roof at each corner and feed wire in a loop around the roof. Bring both ends of the wire, stood off from gutters etc, down into the SGC-237 auto tuner.

You could do this same thing, more effectively even, if you run a manual tuner like a Palstar AT1KP feeding window or open line up to the feed of the loop. That would hold power that way too, good few hundred watts at least.

You'd be able to work reasonably well on any band where the loop was a full wavelength on up in frequency from there. You might be able to get it to play on the next lowest band as well, but losses go up from there.

The other alternative to consider if you have the reach on your property is an end-fed wire with a manual tuner fed against a ground rod with some radials on it. Make the wire a half wavelength or longer for the lowest frequency band you want to work.

Yet another idea is a vertical up on the roof, like a GAP Titan as it requires no radials and will work pretty well from 40m on up...80m on it is pretty useless.

G5RV as mentioned, by its design will be pretty awful lying on a roof. The fan dipole or resonant dipoles would be a lot better than a G5RV for that.

Any antenna that close to the house will pick up a lot of noise from appliances and power supplies inside the house. Of course interference inside the house goes way up with the antenna so close too.