If $2 y = l o g (12 - 5 x - 3 x^{2})$ takes all real values then $x$ belongs to

(- 3, 5 / 3)

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(- 3, 3)

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(- 3, 4 / 3)

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None

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Solution

The correct option is D $(- 3, 4 / 3)$
$2 y = log (12 - 5 x - 3 x^{2})$
$(12 - 5 x - 3 x^{2}) > 0$
$3 x^{2} + 5 x - 12 < 0$
$3 x^{2} + 9 x - 4 x - 12 < 0$
$3 x (x + 3) - 4 (x + 3) < 0$
$(x + 3) (3 x - 4) < 0$
$x ϵ (- 3, 4 / 3)$

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