That's an interesting question. Lots of things affect plant roots. One you probably haven't thought of is the pot a plant is in, if it's a potted plant.

A nursery sold me some plants - they were important to me, because they're named after my grandfather - the 'H. E. McMinn Manzanita'. I planted them in the ground, and then plumbers dug them up later, when I needed a new sewer line. It turned out the roots were bent in the shape of the pot, because the pot was too small for the plant, so there wasn't room for the roots to grow out. So when I planted the plant in the ground, the roots didn't grow out like they would in a healthy plant.

Water, of course, is another thing that affects plants' roots a lot. I take care of my plants, but I could take a lot better care of them. Some of my plants had bad roots, and I didn't know why: Was I watering them too much, and the roots were rotting away from being too wet? Or was I letting them get too dry, and the roots weren't healthy, so the unhealthy roots died when I watered the plant?

My plants are all in pots on my balcony now, and I wish I could see their roots. When I water the pots, the water runs out the bottom really fast, from some of the pots. The water stays in the pot, with other pots. The pots have all different kinds of dirt in them. Sometimes I put thick layers of newspaper in the bottom of the pot before I add the dirt, so the water won't drain out too fast and drip onto the balconies below mine - we're not supposed to let our water drip onto the balconies below!

There's another funny thing about some kinds of dirt. If it gets really really dry, the water doesn't soak in - it just runs off. I had an old bag of potting soil, and the kids were trying to plant plants in it for Mother's Day. But the dirt was so dry that the water wouldn't soak in. In fact, some of the dirt even floated on the water! I was frustrated and disappointed.

The soil or dirt is important for root growth - it needs to hold water but not so long that the roots rot, so there needs to be drainage, too, and air needs to get in. The soil also needs food for the plant, which can be something like compost. My bag of fancy potting soil has lots of strange things in it like worm castings.

But you are asking about roots! I found the following information for you:
here

So I googled this: 'Plant Roots Environment' The most exciting recent research is that roots will grow away from salty soil, even if it means that the roots have to grow in some direction other than down. Normally, roots grow down, in response to gravity.

There are whole conferences and books now about roots and their environments, but I can't find any other general information to give you.