If m x 2 - 9 m x + 5 m + 1 0 and m [ p , q 16 ) , then p + q =

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Solution

Q.
If $m x^{2} - 9 m x + 5 m + 1 > 0$ and $m \in [p, \frac{q}{16})$ , then $p + q =$ _________ .

Ans.
(4)

$m x^{2} - 9 m x + (5 m + 1) > 0$

$\Rightarrow$ $m > 0 and D < 0 \Rightarrow m (61 m - 4) < 0$

$\Rightarrow$ $m \in [0, \frac{4}{61}) \Rightarrow p = 0, q = 4$

$∴$ $p + q = 4$

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