We investigate the influence of Zr and Si segregation on the cohesive strength of grain boundaries (GBs) in molybdenum using density functional theory calculations. A tilt 5(310)[001] and twist 5[001] GB in bicrystal geometry are chosen as structural models. We determine the site preference of Zr and Si for segregation in these GBs and define the segregation energy. We quantify the effect of solutes on the stability of the GBs against brittle fracture by means of the Griffith criterion (work of separation). Additionally, the intrinsic bond strength of the GB containing a solute is quantified by means of the theoretical strength. The results show that Zr and Si tend to segregate at the GBs if the low-energy insertion sites are available. However, the work of separation is decreased by the presence of Zr and Si and even in the presence of oxygen, there is no increase of the Griffith energy. Contributions of strain and chemical energy are analysed in order to explain our findings.