The carrots and potatoes need a longer roasting than the other vegetables. Also, roasting onion keeps it with a relatively "raw" flavor; if you want your onion to taste cooked and lose its sharpness, you should sweat it in oil on a stove before roasting in the case of eating the stuff roasted. If you are going to cook this stuff to a soup, don't roast the onion at all, just sweat it in the pot and then add the roasted vegetables to cook the soup.
Generally, roasting time for nonstarchy vegetables isn't that long. I would start with just the carrots and potatoes (carrots are not starchy, but they are woody and need a long time for the cell walls to break apart and soften; potatoes need some time roasting after the internal temperature has reached 70°C because of the starch). The garlic can also use a long roast, but I would cut it very fine and sweat it together with the onion. That depends on whether you prefer garlic-flavored oil infusing your soup or roasted cloves to bite on.
After the potatoes and carrots have been in the oven (tossed with a little oil) for 25-30 minutes (preferably covered, so they half cook, half roast in their own steam), I would add the tender vegetables (if you want to put the sweated onion in, that's the time for it too). Remove the cover to let the vegetables roast nicely. Then leave in the oven for another 25-30 minutes or until tender.
You won't get the strong roasted flavors of, say, a pepper roasted directly on a flame, but you will have some nicely cooked veggies. You can then cook them up for a very short time in a broth to make a soup (under a minute), or use them in other ways, for example as a side dish, or extending the recipe to become a casserole.
The two-step addition of the vegetables is important, because the tender vegetables like sweet peppers and zucchini become mushy when overcooked and dry when overroasted.
If you want to add spices, add them in the beginning, mixed with the oil. Dried herbs can also be added at the beginning, to have time to rehydrate a bit. Don't add fresh herbs at the beginning, they will wilt. Add them 3-4 min before the final dish (i.e. the soup) is ready.