Help in removing Bouganvilla; do all roots need to come up?

I've got two Bouganvilla's that I'm (trying) to remove:) They're very mature; each has 6-10 two to four inch diameter branches, and some hefty roots, too. I've been digging out around them, and some of the roots go under my walkway, and possibly the foundation. -If I cut the roots off where they go under the walkway, I presume they'll just die off? -Should I be concerned with the dead roots attracting termites, and try to remove them? -How important is it that I get all of the roots up? -Would applying Roundup to the roots themselves help? Thanks!
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