Why is it the case that we take both negative and positive values in the latter but not the former?

Greg mentioned a couple times that ETS only takes the positive root. Would that not be applicable to the second one as well? Or am I missing some difference in the way each one is interpreted by ETS?

this clarifies my doubt about how ETS views roots, thank you!
just wondering, would this mean that the second question i posted would then have C as the answer? although i am also wondering how (a-b) squared and (b-a) squared both would have the same expansion and it can be interpreted either ways.