Number of integral values of ' x ' such that | x 2-3 x -10|+|11 x - x 2-10|=|8 x -20|, is

Question

Number of integral values of ' x ' such that | x 2-3 x -10|+|11 x - x 2-10|=|8 x -20|, is (A) 7 (B) 8 (C) 9 (D) 10

Tardigrade Admin · Accepted Answer

(x2-3 x-10)(11 x-x2-10) ≥ 0 ∴(x2-3 x-10)(x2-11 x+10) ≤ 0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e197612e41b6e19903ea79d5e3667854-.png" /> ⇒(x-5)(x+2)(x-1)(x-10) ≤ 0 x=-2,-1,0,1,5,6,7,8,9,10

Q. Number of integral values of ' $x$ ' such that $∣ ∣ x^{2} - 3 x - 10 ∣ ∣ + ∣ ∣ 11 x - x^{2} - 10 ∣ ∣ = ∣8 x - 20∣$ , is

7

8

9

10

$(x^{2} - 3 x - 10) (11 x - x^{2} - 10) \geq 0$
$∴ (x^{2} - 3 x - 10) (x^{2} - 11 x + 10) \leq 0$

$\Rightarrow (x - 5) (x + 2) (x - 1) (x - 10) \leq 0$
$x = - 2, - 1, 0, 1, 5, 6, 7, 8, 9, 10$

Q. Number of integral values of ' x ' such that ∣∣​x2−3x−10∣∣​+∣∣​11x−x2−10∣∣​=∣8x−20∣, is

7

8

9

10

(x2−3x−10)(11x−x2−10)≥0 ∴(x2−3x−10)(x2−11x+10)≤0 ⇒(x−5)(x+2)(x−1)(x−10)≤0 x=−2,−1,0,1,5,6,7,8,9,10

Q. Number of integral values of ' $x$ ' such that $∣ ∣ x^{2} - 3 x - 10 ∣ ∣ + ∣ ∣ 11 x - x^{2} - 10 ∣ ∣ = ∣8 x - 20∣$ , is

$(x^{2} - 3 x - 10) (11 x - x^{2} - 10) \geq 0$
$∴ (x^{2} - 3 x - 10) (x^{2} - 11 x + 10) \leq 0$

$\Rightarrow (x - 5) (x + 2) (x - 1) (x - 10) \leq 0$
$x = - 2, - 1, 0, 1, 5, 6, 7, 8, 9, 10$