The greatest positive integral value of $x$ for which $200 - x (10 + x)$ is positive is

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Solution

The correct option is B 9
$200 - x (10 + x)$

$= 200 - 10 x - x^{2}$

$= 200 - 20 x + 10 x - x^{2}$

$= 20 (10 - x) + x (10 - x)$

$= (20 + x) (10 - x)$

$\Rightarrow f (x) > 0 \forall x ϵ (- 20, 10)$

$∴$ greatest positive integral value for which $f (x) > 0$ is $x = 9$ ( $∵$ at $x = 10, f (x) = 0$ )

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