Theory of Equations 5 Question 16
16. For $k>0$, the set of all values of $k$ for which $k e^{x}-x=0$ has two distinct roots, is
(a) $0, \frac{1}{e}$
(b) $\frac{1}{e}, 1$
(c) $\frac{1}{e}, \infty$
(d) $(0,1)$
True/False
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Answer:
Correct Answer: 16. (a)
Solution:
- For two distinct roots, $1+\ln k<0(k>0)$
$ \ln k<-1 \Rightarrow \quad k<\frac{1}{e} $
Hence, $k \in 0, \frac{1}{e}$
