Mixed methods research is viewed as the third methodological movement that emerged in response to the limitations

Mixed methods research is viewed as the third methodological movement that emerged in response to the limitations of quantitative or qualitative methods alone. While the purists’ view of the dichotomy between positivist and constructivist philosophies is prevalent, mixed methods research affords researchers an opportunity to use a more pragmatic approach to answer the research question.
Mixed Methods is a research methodology that draws on potential strengths of both qualitative and quantitative methods. This research approach requires a purposeful mixing of methods in data collection, data analysis and interpretation of the evidence. The key word is mixed, as an essential step in the mixed methods approach is purposeful  integration of data at an appropriate stage in the research process. Purposeful data integration enables researchers to seek a more panoramic view of phenomena from different viewpoints and through diverse research lenses.

Qualitative Research

underlying philosophy of Constructivism (also known as Idealism)
considers knowledge (reality) to be ‘constructed’ (i.e., shared meaning or interpretation of the nature of being in the world)
constructions are subjective (i.e., subject to individual interpretation)
uses inductive reasoning (research-then-theory approach) where 1. categories/themes emerge from the data during analysis, and 2. categories/themes play an active role in development of theory

Quantitative Research

underlying philosophy of Positivism (also known as Naturalism)
considers knowledge to be created by application of natural science methods

knowledge is objective based on: 1. empiricism (knowledge based on empirical observation); 2. testing and verification of theories, and 3. development of universal laws
uses deductive reasoning (theory-then-research approach) where: 1. research design is tightly structured and 2. research questions are highly specific (usually formulated as hypotheses)

I am one of those nurse researchers who has conducted research using both Qualitative and Quantitative methodologies, as well as a third methodology called Mixed Methods.  Read a bit about the philosophy of this Mixed Methods research method below.
Mixed Methods Research

does not adhere to particular approaches based on philosophical underpinnings
combines Quantitative and Qualitative research methods
requires a pragmatic approach to research where research design is seen as a choosing of methods that best facilitate understanding of a problem

Ref:
UKEssays. (November 2018). Comparison of Qualitative and Quantitative Research Methods. Retrieved from https://www.ukessays.com/assignments/qualitative-quantitative-research-methods