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Properties of Inequalities

The least int...

Question

The least integral value of $x$ , which satisfy the inequality $\frac{x^{2} - 3 x + 4}{x^{2} - 6 x + 8} \leq 0$ is

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Solution

$\frac{x^{2} - 3 x + 4}{x^{2} - 6 x + 8} \leq 0$
$\Rightarrow \frac{x^{2} - 3 x + 4}{(x - 4) (x - 2)} \leq 0$

We know that,
$x^{2} - 3 x + 4 > 0 ∵ D = 9 - 12 < 0$
The critical points are $2, 4$
$∴ x \in (2, 4)$

Hence, the least integral value of $x$ is $3$ .

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Properties of Inequalities

Standard XII Mathematics

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