Which aquatic plant can produce roots and shoots at its nodes?

Water Smartweed is the correct choice because it is known for its ability to produce both roots and shoots at its nodes. This characteristic allows Water Smartweed to propagate efficiently in aquatic environments. The nodes, which are the points along the stem where leaves and branches originate, serve as sites for new growth. This means that when a piece of the plant is broken off or disturbed, it can establish itself in a new location, thus enabling the species to spread quickly in suitable habitats.

In contrast, the other options do not exhibit this same regenerative trait to the same extent. American Frogbite primarily reproduces through floating leaves and does not have the same extensive propagation ability via nodes. Eurasian Watermilfoil can reproduce vegetatively but does so mainly through fragmentation of the stems rather than forming new shoots and roots at designated nodes. Duck-lettuce, while also a valuable aquatic plant, predominantly reproduces through seeds rather than through a robust node system that allows for the development of roots and shoots in the manner that Water Smartweed does.