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 $b ?$
Solution:
If $f(x)$ is a polynomial such that $f(a) f(b)<0$ then this means the value of the polynomial are of different sign for $a$ to $b$
Hence, at least one zero will be lying between $a$ and $b$