The equation x^3 + x - 1 = 0 has

MHT CET 2023 Mathematics question

Mathematics Application of Derivatives MHT CET 2023

The equation has

(A)no real root
(B)exactly two real roots
(C)exactly one real rootCorrect
(D)all three real roots

Answer: (C)

Solution

Let . Then for all real , so is strictly increasing and can cross the x-axis at most once. Also and , so by the intermediate value theorem there is a root in . Hence there is exactly one real

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Question ID VK-094616