The range of p for which the equation e x = px has two real solutions is

Question

The range of p for which the equation e x = px has two real solutions is (A) (0, e) (B) (1, e) (C) (1, ∞) (D) (e, ∞)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/554516019a1156490c7f306d3af4a45d-.png" /> ( e x / x )= e x ⇒ x =1 ⇒ m = e ∴ text for two real solution p ∈( e , ∞)

Q. The range of $p$ for which the equation $e^{x} = p x$ has two real solutions is

$(0, e)$

$(1, e)$

$(1, \infty)$

$(e, \infty)$

$\frac{e ^{x}}{x} = e^{x} \Rightarrow x = 1$
$\Rightarrow m = e$
$∴ for two real solution p \in (e, \infty)$

Q. The range of p for which the equation ex=px has two real solutions is

(0,e)

(1,e)

(1,∞)

(e,∞)