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If f(x) is a polynomial such that f(a)f(...

If `f(x)` is a polynomial such that `f(a)f(b)<0`, then what is the number of zeros lying between `a` and ` b`?

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`f(x)` is a polynomial such that `f(a)f(b)<0` implies that one of them must be negative and other must be positive.
The graph of f(x) must be on the both sides of the x axis i.e above or below the x -axis.
Thus, graph of f(x) should cut the x –axis at least once in between a and b.
Therefore, no. of zeroes of f(x) between a and b is at least one.
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