x^2-15x-101=0
Positive: +-- = 1
Negative: ++- =1
Imaginary: 0
from rational root theorem candidates are: +/-101 and +/-1
but none of them satisfy the given equation therefore there are no rational roots and no imaginary roots,
hence we can find the irrational roots using quadratic formula.
and on applying quadratic formula we get:
x = 1/2 (15 - sqrt(629)) or 1/2 (15 + sqrt(629))