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Finite and Infinite Sets

Let S be the ...

Question

Let S be the set of all values of x such that $l o g_{2 x} (x^{2} + 5 x + 6) < 1$ then the sum of all integral value of x in the set S, is

A

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B

8

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D

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Solution

The correct option is D 0
$l o g_{2 x} (x^{2} + 5 x + 6) < 1$

$\Rightarrow x^{2} + 5 x + 6 < 2 x^{1}$

$\Rightarrow x^{2} + 3 x + 6 < 0$

But $x^{2} + 3 x + 6 = 0$ has no real roots

$∴ S$ is an empty set

$∴$ sum of all integral values of $x = 0$

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