Auxin is a growth plant hormone that helps in apical elongation and growth of meristematic tissues.
Cytokinin are plant hormones that are responsible for the process of cell division and cell differentiation.
Auxins induce meristematic cell division, while cytokinin induces differentiation of cells for inhibiting the meristematic activity of auxin.
Auxins promote the root differentiation of root cells and their cell division, elongation, and callus formation, while cytokinin is involved in the induction the cell differentiation and division when there are intermediate levels of both hormones.
Hence, shoot formation is favored when there is a high ratio of cytokinin to auxin.
Whereas, the root formation is favored when there is a high ratio of auxin to cytokinin.