Let f x be a non-constant polynomial such that f a = f b = f c = 2 . Then the minimum number of roots of the equation f " x = 0 in x ∈ a , c is/are

Step-by-step solution

As f a = f b = f c , then by Rolle’s theorem, we get, f c 1 = f c 2 = 0 ⇒ for some c 1 ∈ a , b & c 2 ∈ b , c Again, applying Rolle’s theorem to function y = f ' x , we have f " c = 0 for some c 3 ∈ c 1 , c 2 Hence, the equation f " x = 0 has at least one root.