AMC 12B #24

[stupidityismygam]

The set of real numbers [unparseable or potentially dangerous latex formula] for which
[unparseable or potentially dangerous latex formula]
is the union of intervals of the form [unparseable or potentially dangerous latex formula]. What is the sum of the lengths of these intervals?

[sinkokuyou]

since it's asking for a range, the 2010 doesn't really matters...
so we have
[unparseable or potentially dangerous latex formula]
and it turns out to be:
[unparseable or potentially dangerous latex formula]
and after sorting it, you'll have a inequalty
[unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]
So the sum of the roots is 3.
Each interval is (-1, something), (0, something), (1, something),
so the total length is something+something+something, which is the sum of the roots.
So it's 3.