Number of integral values of $x$ satisfying $| x^{2} - 5 x + 4 | = 2$ is

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Solution

$| x^{2} - 5 x + 4 | = 2$
$\Rightarrow x^{2} - 5 x + 4 = 2 or x^{2} - 5 x + 4 = - 2 \Rightarrow x^{2} - 5 x + 2 = 0 or x^{2} - 5 x + 6 = 0 \Rightarrow x = \frac{5 \pm \sqrt{25 - 4 \times 2}}{2} or (x - 3) (x - 2) = 0 \Rightarrow x = \frac{5 \pm \sqrt{17}}{2} or x = 3, 2$

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