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

Question

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?

Philoid · Accepted Answer

Let’s first draw the figure,

As we can see in the figure the number of zeroes can be 1 or 3.

So the least numbers of zeroes lying between a and b is 1.