To determine whether a function f(x) has any zeros in a given interval, the Intermediate Value Theorem can be applied. This theorem states that if a function is continuous on a closed interval [a, b] and takes on different signs at the endpoints (i.e., f(a) and f(b) have opposite signs), then there is at least one c in the interval (a, b) such that f(c) = 0.
In simpler terms, if you start with a value of f(a) that is positive and move to f(b) which is negative, the function must cross the x-axis at least once within that interval, indicating a zero exists. The key requirement here is the continuity of the function; if the function is not continuous, then the theorem does not guarantee the presence of zeros.