The molecular genetic mechanisms by which plants modulate their root growth rate (RGR) in response to nutrient deficiency are largely unknown. Using a panel of Arabidopsis thaliana natural accessions, we provide a comprehensive combinatorial analysis of RGR variation under macro- and micronutrient deficiency, namely phosphorus (P), iron (Fe), and zinc (Zn), which affect root growth in opposite directions. We found that while -P stimulates early RGR of most accessions, -Fe or -Zn reduces it. The combination of either -P-Fe or -P-Zn leads to suppression of the growth inhibition exerted by -Fe or -Zn alone. Surprisingly, Arabidopsis reference accession Columbia (Col-0) is not representative of the species under -P and -Zn. Using a genome wide association study, we identify candidate genes that control RGR under the assayed nutrient deficiency conditions. By using a network biology driven search using these candidate genes, we further identify a functional module enriched in regulation of cell cycle, DNA replication and chromatin modification that possibly underlies the suppression of root growth reduction in -P-Fe conditions. Collectively, our findings provide a framework for understanding the regulation of RGR under nutrient deficiency, and open new routes for the identification of both large effect genes and favorable allelic variations to improve root growth.