I understand that trace element behavior in a system depends on whether they are compatible or not. But , if that question is asked in an examination , what could be the points that one should write to answer that?
Not much of anything, trace elements are found in low concentrations in the mantle because they are lithophobic. During crystallisation they end up in the residue of silica, and incompatible elements like gold etc..., that is squeezed out into the country rock around the margins of igneous intrusions.
What is the role of trace elements in magmatic crystallization?
They don't really have a role in magmatic crystallisation. Trace elements are useful because they are (sometimes) more sensitive to changes in crystallisation conditions, when they are measured.
For example, a basalt crystallising plagioclase wouldn't change its Al, Ca, Na, and Si contents too much. They will change a bit, but nothing serious. On the other hand, strontium and europium are two trace elements that are extremely compatible in plagioclase. Seeing a rock with a strong depletion of Eu and Sr compared to average crust (for example) indicates that plagioclase has crystallised in its crystallisation history. This is less obvious when considering only major elements (although can be deduced by the experienced petrologist).