The word qualitative implies an emphasis on the qualities of entities and on processes and meanings that are not experimentally examined or measured [if measured at all] in terms of quantity, amount, intensity, or frequency. Qualitative researchers stress the socially constructed nature of reality, the intimate relationship between the researcher and what is studied, and the situational constraints that shape inquiry... 

Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques. Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon...

Mixed methods research is the type of research in which a researcher or team of  researchers combines elements of qualitative and quantitative approaches (e.g., use of qualitative and quantitative viewpoints, data collection, analysis, inference techniques) for the purpose of breadth and depth of understanding and corroboration...

You can analyse your chosen topic with several different methods of analysis of the same generic type, i.e. either qualitative or quantitative. This kind of research strategy is called multi-method research. If you use both qualitative and quantitative methods, that is mixed method research. If you apply just a single method of analysis to a research project, you may produce results giving only a limited understanding of a large phenomenon. You can adjust the research process by selecting several methods to analyse the chosen phenomenon. Multi-method analysis increases the possibilities of getting varied and extensive results...

UX research—or as it’s sometimes called, design research—serves many purposes throughout the design process. It helps us identify and prove or disprove our assumptions, find commonalities across our target audience members, and recognize their needs, goals, and mental models. Overall, research informs our work, improves our understanding, and make our work better...