Final answer:
The missing organelle in a mutant plant with roots that grow in all directions is the amyloplast, which is responsible for detecting gravity and guiding root growth.
Step-by-step explanation:
In a mutant plant where roots grow in all directions, the organelle that you would expect to be missing in the cell is the amyloplast. Amyloplasts are a type of plastid that serve as gravity sensors within plant cells, particularly in root cells, and they assist in directing roots to grow downward by responding to gravitational pull. Due to the critical role of amyloplasts in gravitropism—the growth response of a plant to gravity—a plant without these organelles would have roots that grow in random directions rather than anchoring into the soil appropriately.