All Buddhist teachings revolve around the same core, Dependent Co-Arising, usually described as the Twelve Nidanas.
Dependent Co-Arising refers to the process of development of informational (representational, semiotic) reality, starting with unconscious causational/informational tendencies, to basic inclings of rudimentary representation, to development of mind, to emergence of representational "entities", culminating in an idea of Self as Subject of experience and Agent of action.
This process grows hand-in-hand with (co-develops in conjunction with) development of behavioral tendencies for attraction, repulsion, and judgement in general (of things as "good" and "bad"). When these two things - the representational reality made up of entities and self - and the judgement-based attraction/repulsion - come to maturity, we end up having something that thinks of itself as a sentient being acting in a world of good and bad entities, trying to acquire the good, and get rid of the bad. But because the fundamental assumption this is all based on is false - because in fact the world is not made of fixed entities, and they are not inherently good (desirable) or bad (undesirable), this situation leads to all kinds of turbulence, that to these so-called "sentient beings" looks like a valid struggle against trouble and suffering, towards some imagined idealized happy state. The funny thing though is, the more each of these "sentient beings" acts to obtain happiness for itself, the more trouble they (us) create for each other, and therefore for all of them (us). So to them (us) it looks like they (we) are trying hard to make things better, but in fact they (we) end up perpetuating this confusion and struggle.
This situation is the core condition of the vast amount of uninstructed worldlings. They (we) think their (our) subjective idea of the world is what the world is, and they (we) seriously try to act within it, only causing more trouble, endlessly.
The Three Roots are a distilation of the above to three basic tendencies in the minds of sentient beings. A tendency for assuming something as desirable, a tendency for assuming something as undesirable, and a tendency for taking subjective (representational) things at the face value as if they were objective.
It's kinda sad, if you think about it. Even tragic, if you ask me. Out of this vast field of energy develop formations capable of representation, and then these formations seriously think they need a new cell phone or a bigger breast. It would be comical if it weren't so sad.