There is increasing evidence that cancer stem cells (CSC) are more radioresistant than differentiated cancer cells (DCC). Radiation treatment of solid tumors can induce long-term enrichment of CSC, which can lead to resistance and a loss of sensitivity to radiotherapy. At the same time, radiation-induced reprogramming of DCCs into CSCs has also been observed. Using a mathematical model, we study the dynamics of CSCs and DCCs with reprogramming induced by radiation therapy. We also investigate the effect of feedback on cell division rates together with reprogramming, and renewal probability. We observe that feedback on cell division rates results in long-term enrichment of CSC whereas the effect of feedback on self-renewal probabilities results only in short-term CSC enrichment even when there is reprogramming. In the context of glioblastoma, we find there is an optimal choice of dose fractionation to reduce CSC percentages and tumor sizes.