If 4a + 2b + c = 0 then the equation 3ax^2 + 2bx + c = 0 has at least one real root lying between

JEE Advanced Mathematics question

If then the equation has at least one real root lying between

Answer: (C)

Consider , whose derivative is . Then

g(0) = 0, g(2) = 8a + 4b + 2c = 2(4a + 2b + c) = 0 .

By Rolle's theorem, has a root in .

(a) and (b) are not guaranteed: e.g. $a = 1, b = -2, c =

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Question ID VK-109442