Question

# The equation ex−1 + x - 2 = 0 has

A
one real root
B
two real roots
C
three real roots
D
four real roots.

Solution

## The correct option is A one real rootClearly, x = 1 satisfies the given equation. Assume that f(x) = ex−1 + x − 2 = 0 has a real root α other than x = 1. We may suppose that α > 1 (the case α < 1 is exactly similar). Applying Rolle's theorem on [1, α] (if α < 1 apply the theorem on[α, 1]), we get β ϵ (1, α) such that f'(β) = 0. But f′(β) = eβ − 1 + 1, so that eβ − 1 = −1, which is not possible. Hence there is no real root other than 1.Mathematics

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