Find the roots of the equation x^2 +111.11x+1.2121=0 by hand using the quadratic formula using base 10 and mantissa length 5. Then, find the same roots using the formula x= (-2c)/(b+-sqrt(b^2=4ac)).

The true roots of this equation are -1.1110X10^2 and -1.0910 X 10^-2. Explain the differences in the calculated roots and the true roots. What causes these differences?