Background
The authors say "it has been reported that tomato plants grown under elevated CO2 have greater total root length, root surface area, root diameter, root volume and number of lateral roots than those under ambient CO2, leading to a greater root system," citing Wang et al. (2009). And they indicate that "as a result, elevated CO2 significantly increased the uptake of N, P, K, Ca, Mg and micronutrients (Cu, Fe, Mn and Zn)," which in turn was found to have promoted "plant growth and development (Prior et al., 1998)."

What was done
In a study designed to further explore this phenomenon, Wang et al. (2013) assessed the lateral root production of 19-day-old tomato (Solanum lycopersicum) seedlings grown in basal nutrient solution for an additional four days under hydroponic conditions in the laboratory at atmospheric CO2 concentrations of either 350 or 800 ppm.

What was learned
Consistent with the findings of Wang et al. (2009), the seven scientists found that the number of lateral roots increased by 75% under elevated CO2 compared to ambient CO2 and that the length of the roots increased as well.

What it means
With more and longer lateral roots in a future CO2-enriched atmosphere, tomato plants (and likely other plants as well) should be better equipped to take up both major and micro nutrients from the soils in which they grow, making them both bigger and better and more apt to produce larger and more nutritious fruit ... and more of it.

References
Prior, S.A., Torbert, H.A., Runion, G.B., Mullins, G.L., Rogers, H.H. and Mauney, J.R. 1998. Effects of carbon dioxide enrichment on cotton nutrient dynamics. Journal of Plant Nutrition 21: 1407-1426.

Wang, Y., Du, S.T., Li, L.L., Huang, L.D., Fang, P., Lin, X.Y., Zhang, Y.S. and Wang, H.L. 2009. Effect of CO2 elevation on root growth and its relationship with indole acetic acid and ethylene in tomato seedlings. Pedosphere 19: 570-576.