(B) We have the inequality: $9 x-2

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(B) We have the inequality: $9 x-2 This can be split into two parts: Part $I$: $9 x-2 $9 x-2 $x^2-5 x+6 > 0$ $(x-3)(x-2) > 0$ So, $x \in (-\infty, 2) \cup (3, \infty)$ ... $(i)$ Part $II$: $(x+2)^2 $x^2+4 x+4 $x^2-8 x+7 $(x-7)(x-1) So, $x \in (1, 7)$ ... $(ii)$ Taking the intersection of $(i)$ and $(ii)$, we get: $x \in (1, 2) \cup (3, 7)$ The integral values of $x$ in this interval are $\{4, 5, 6\}$. Thus, the number of integral values is $3$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic inequations and Newton Formula

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The number of integral values of $x$ satisfying $9 x-2 < (x+2)^2 < 12 x-3$ is

TS EAMCET 2020 All TS EAMCET

A
not finite
B
$3$
C
$4$
D
$5$

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