Why do auxins have an opposite effect on roots?Why do auxins accumulate in the shady side,what will happen if they accumulate towards sun/light?

Auxins promote growth of roots and stimulate them to grow downwards and deeper. It enhances root elongation as well as branching or development of adventitious roots. In roots, the effect of auxins differ from that of shoots. In root cells, the shaded portion contains more auxin but it grows less than the portion of light. This is due to the phenomena of negative phototropism shown by roots which causes roots to bend away from light.
Auxin accumulates only in the shaded side of the plant because it gets destroyed by sunlight.

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