Taking zinc supplements could help reduce period of suffering due to common cold in adults but the same effect was not found in children.

However they did not lessen the severity of the symptoms or had any effect on children while nausea or bad taste was a common complaint among those who took the supplements. “Although oral zinc can impact the duration of [the] common cold in adults, there is not enough evidence to recommend its use in children, and only a weak rationale for its use in adults”, Dr Science said.
Source-Medindia