The Equation ex – 1 + x – 2 = 0 As

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Question

The equation e^x^–¹ + x – 2 = 0 as

easy

Solution

Correct option is

one real root

Clearly, x = 1 satisfies the given equation. Assume that f (x) = e^x^{– 1} + x – 2 = 0 has a real root α other than x = 1. We may suppose that

a > 1 (the case a < 1 is exactly similar). Applying Roll’s theorem on [1, α] (if α < 1 apply the theorem on [α, 1]), we get β

Which is not possible. Hence there is no real root other than 1.

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