The complete set of non-zero values of k such that the equation |x2-10 x+9|=k x is satisfied by atleast one and atmost three values of x, is

Question

The complete set of non-zero values of k such that the equation |x2-10 x+9|=k x is satisfied by atleast one and atmost three values of x, is (A) (-∞,-16] ∪[4, ∞) (B) (-∞,-16] ∪[16, ∞) (C) (-∞,-4] ∪[4, ∞) (D) (-∞, 4] ∪[16, ∞)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/fe2b7b1533cdfbbe869064ee21067490-.png" / From the graph (-∞,-16] ∪[4, ∞)

Q. The complete set of non-zero values of $k$ such that the equation $∣ ∣ x^{2} - 10 x + 9 ∣ ∣ = k x$ is satisfied by atleast one and atmost three values of $x$ , is

$(- \infty, - 16] \cup [4, \infty)$

$(- \infty, - 16] \cup [16, \infty)$

$(- \infty, - 4] \cup [4, \infty)$

$(- \infty, 4] \cup [16, \infty)$

From the graph $(- \infty, - 16] \cup [4, \infty)$

Q. The complete set of non-zero values of k such that the equation ∣∣​x2−10x+9∣∣​=kx is satisfied by atleast one and atmost three values of x, is

(−∞,−16]∪[4,∞)

(−∞,−16]∪[16,∞)

(−∞,−4]∪[4,∞)

(−∞,4]∪[16,∞)