@dharr @Carl Love thanks for your responses! My question is not so much how to use Maple to distinguish the roots, or how to achieve some specific goal. Rather, I am pretty astonished that Maple can do this, and I am just curious about how Maple does this! I imagine that, to distinguish them, it has to pick some embedding of the splitting field of the polynomial into the complex numbers. Such an embedding always exists, but there are as many as n! embeddings (if n is the degree of the polynomial).

It's all well and good for us to say "just pick one", how does Maple actually algorithmically do this? Or does it do something different?