Final answer:
Root slices of a carrot can give rise to new plants due to totipotent cells in the root apical meristems that can differentiate into any type of cell required for plant development.
Step-by-step explanation:
The cells in the root of a carrot that can give rise to an entire plant possess a characteristic known as totipotency. Totipotent cells have the remarkable ability to differentiate into any kind of cell necessary for the growth and development of an organism. In the context of plant biology, the parenchyma cells within carrot roots are able to de-differentiate and resume an embryonic condition, which allows them to divide and transform into a variety of specialized cells, leading to the formation of a new, complete plant. This is possible because of the presence of root apical meristems, which are embryonic regions that continually produce new cells, allowing for the elongation of the root and shoot, through a process known as primary growth.