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BITSAT2015MathematicsApplication of DerivativesActual

The number of real roots of the equation e e ^ (x-1) + x -2=0 is

Options

  1. A1
  2. B2
  3. C3 3
  4. D4

Correct answer

A. 1

Step-by-step solution

Let f(x)=e^ x-1 +x-2 check for x=1 Then, f (1)= e ⁰+1-2=0 So, x=1 is a real root of the equation f(x)=0 Let x= be the other root such that >1 or 0, for all x . Thus f ^ ( x ) 0, for any x (1, ) or x ( , 1) which is a contradiction. Hence, f ( x )=0 has no real root other than 1 .

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