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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)

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