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When there is no root in the given interval, the function find_root() does not return anything but raises a RuntimeError exception:

sage: f(x) = 2 ; f
x |--> 2
sage: find_root(f,-10,10)
...
RuntimeError: f appears to have no zero on the interval

If you want to deal with that, you have to catch the error (otherwise your program will stop here):

try:
    root = find_root(f,-10,10)
    root_exist = True
except RuntimeError:
    root_exist = False

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