GATE 2015 EE – SET 1 – Question 2

Solution: As f(x) is continuous in [a,b] and f(x) has no root in [a,b], f(x) does not cut x axis for all x in [a,b]

$$\Rightarrow f(x)$$ is either above x axis or below x axis for both x=a and x=b

$$\Rightarrow$$ f(a) and f(b) are both positive or both negative

$$\Rightarrow$$ f(a).f(b) >0

Hence, the correct option is (C)