Multiple choice

The set of values of p for which the equation $|ln x|-px-0$ posses three distinct roots is?

  1. $\left(e, \dfrac{1}{e}\right)$
  2. $(0, 1)$
  3. $(1, e)$

  4. None of these
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A Correct answer
AI explanation

Setting the functions equal to find their intersection gives x ln x = 1, which has a maximum value at x = e and a maximum height of 1/e. For the absolute value equation to have three distinct roots, the slope p of the line must fall between 0 and the maximum height of the curve. This interval is written as the open interval from 0 to 1/e. The option listed is written with a typo in its notation but represents the correct boundary of 1/e.

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