They were so brilliant and curious!
Here is the answer!
Yes, you can grow plants in zero gravity, though there is one complication.
A plant grown on the International Space Station:
The complication that needs to be overcome is that plants make use of gravity when planted to orient themselves (as they can't rely on being planted the right way up), so that their roots go down and their sprouts go up. Without gravity, they will tend to just stay at around the same depth and not sprout. One astronaut reported that this was simple enough to fix, however, just by plucking the ends out of the soil, pulling them to the surface, when they first sprout. From this point, the plant can orient itself using light and will continue to grow. Roots don't suffer as much, as they just grow away from the seed and avoid light (the surface), so develop relatively normally.
After this, growth is mostly normal (as can be seen above). The resulting plants can look a little unusual because they don't have the usual drooping from gravity, so will tend to be more upright.