The zeroth–order general Randić index, 0 R α (G), of a connected graph G, is defined as 0 R α (G) = n i=1 d α i , where d i is the degree of the vertex v i of G and α arbitrary real number. We consider linear combinations of the 0 R α (G) of the form 0 R α (G) − (∆ + δ) 0 R α−1 (G) + ∆δ 0 R α−2 (G) and 0 R α (G) − 2a 0 R α−1 (G) + a 2 0 R α−2 (G), where a is an arbitrary real number, and determine their bounds. As corollaries, various upper and lower bounds of 0 R α (G) and indices that represent some special cases of 0 R α (G) are obtained.