The set of value(s) for K for which the equation |x2-5| x|+6|=2 K has eight real and distinct solution is

Question

The set of value(s) for K for which the equation |x2-5| x|+6|=2 K has eight real and distinct solution is (A)  0  (B) [0, (1/8)] (C) (0, (1/8)) (D) (0, (1/16)]

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/879987f858f4d0215b9ded3e570ee1f4-.png" /> | x 2-5| x |+6|=2 K has eight real and distinct solutions, then 0<2 K <(1/4) 0< K <(1/8)

Q. The set of value(s) for $K$ for which the equation $∣ ∣ x^{2} - 5 ∣ ∣ x ∣ + 6∣ = 2 K$ has eight real and distinct solution is

${0}$

$[0, \frac{1}{8}]$

$(0, \frac{1}{8})$

$(0, \frac{1}{16}]$

$∣ ∣ x^{2} - 5 ∣ ∣ x ∣ + 6∣ = 2 K$ has eight real and distinct solutions, then
$0 < 2 K < \frac{1}{4}$
$0 < K < \frac{1}{8}$

Q. The set of value(s) for K for which the equation ∣∣​x2−5∣∣​x∣+6∣=2K has eight real and distinct solution is

{0}

[0,81​]

(0,81​)

(0,161​]