For the equation \( \frac{e^{-x}}{1+x}=\lambda \) which of the following statement(s) is/are cor...

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For the equation \( \frac{e^{-x}}{1+x}=\lambda \) which of the following statement(s) is/are correct ?
(a) When \( \lambda \in(0, \infty) \) equation has 2 real and distinct roots
(b) When \( \lambda \in\left(-\infty,-e^{2}\right) \) equation has 2 real and distinct roots
(c) When \( \lambda \in(0, \infty) \) equation has 1 real root
(d) When \( \lambda \in(-e, 0) \) euqation has no real root
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