If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?

A. f(a) $$ \cdot $$ f(b) = 0

B. f(a) $$ \cdot $$ f(b) < 0

C. f(a) $$ \cdot $$ f(b) > 0

D. $$\frac{{{\text{f}}\left( {\text{a}} \right)}}{{{\text{f}}\left( {\text{b}} \right)}} \leqslant 0$$

Answer: Option C