Let the values of x which satisfy the inequalities $x^{2} - 3 x + 2 > 0$ and $x^{2} - 3 x - 4 \leq 0$ be $[m, n) (p, q]$ .Find $m + n + p + q$ ?

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Solution

$x^{2} - 3 x + 2 > 0$ and $x^{2} - 3 x + 2 \leq 0$
$∴ (x - 1) (x - 2) > 0 \Rightarrow x < 1, x > 2$ ...(1)
and $(x + 1) (x - 4) \leq 0 \Rightarrow - 1 \leq x \leq 4.$ ...(2)
Thus from (1) and (2), $x \in [- 1, 1) \cup (2, 4] .$

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