What do you see as the main differences between these two approaches? qualitative and quantitativediscuss the two methodological approaches,...

If you are just talking about these types of approach in
general social science research, qualitative research is less accurate and "provable"
whereas quantitative research can be less true to the reality of the situation that you
are studying.

For example, quantitative researchers in
political science might study the impact of the demographics of Congresspeople's
districts on their votes.  They would do this using pure numbers.  They could then claim
to demonstrate that the level of income in the district had a 50% impact on the way the
representative voted on some issue.  A qualitative research project would not use
numbers so much.  It would interview Congresspeople, perhaps, to ask what influences
them to vote the way that they do.

In this case, the
qualitative interview subjects might not be aware of the impact of their constituents'
incomes on their votes.  Or they might not want to admit it.  This would make the
quantitative approach more accurate.  However, it might not be useful to know the
statistical correlation between income and vote.  It might be more useful to know what
the representatives think they are doing and what thoughts
actually go on in their heads.  In this way, the qualitative approach might do a better
job of portraying the human aspect of the decisions that are being
made.