Once they germinate, beet and carrot seeds need to be thinned so that roots have ample space to develop. Both carrots and beets need 3 to 4 inches between seedlings. You can thin them in two stages. First, thin roots to 1 to 2 inches apart a couple of weeks after germination. Next, make the final cut. Eliminate weaker seedlings that have less root growth. Failure to thin, or not thinning enough, leaves the seeds too little room to grow roots.
While you can plant successive beet and carrot crops, continuing to sow seeds too late in the year can leave you with plants that do not form roots. Hot weather can restrict the root formation in these cool-weather veggies. If you've thinned seeds and are still experiencing root problems, or are experiencing long periods of hot weather, the season is likely the culprit.
If your garden soil is hard or compacted, this could play a role in your gardening woes. Beet and carrot roots need to push through the soil as they grow. With extremely dense or compacted soils, this is not easy. In a hard clay soil, you would have better luck with short carrot varieties and beets than with long carrot varieties. Loose, well-draining soils offer friendlier germinating ground for these crops.
Root vegetables fare best in beds with little weed competition. Hand-weed your garden bed to cut down on competitors and encourage root growth. Avoid using tools or hoe very shallowly so you don't damage growing vegetables. You can start planting both beet and carrot seeds about two weeks before the last frost date in your area. At this time, soil temperatures measure 50 to 60 degrees Fahrenheit.