The Equation ex – 1 + x – 2 = 0 As 

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Question

The equation e 1 + x – 2 = 0 as 

Solution

Correct option is

one real root

Clearly, x = 1 satisfies the given equation. Assume that (x) = ex – 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.

Testing

SIMILAR QUESTIONS

Q1

The curve y = ax3 + bx2 + cx + 8 touches x – axis at P(2, 0) and cuts they – axis at a point Q where its gradient is 3. The value of a, b, c are respectively

Q2

If the tangent at (1, 1) on y2 = x(2 – x)2 meets the curve again at P, is

Q3

The tangent to the curve 

At the point corresponding to  is

Q4

The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are

Q5

 the in this interval

Q6

The set of all values of a for which the function

                   

decreases for all real x is

Q7
Q8

The length of a longest interval in which the function 3 sin x – 4Sin3x is increasing is

Q10

The function f satisfying