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# The inequality $$\Large 2x^{2} + 9x + 4 < 0$$ is satisfied for which of the following values of 'x'?

 A) $$\Large - 4 < x - \frac{1}{2}$$ B) $$\Large \frac{1}{2} < x < 4$$ C) 1 < x < 2 D) - 2 < x < 1

 A) $$\Large - 4 < x - \frac{1}{2}$$

Description for Correct answer:
$$\Large 2x^{2} + 9x + 4 = 0$$

x = $$\Large\frac{ -(9) \pm \sqrt{(9)^{2} - 4 \times 2 \times 4}}{2 \times 2}$$

= $$\Large \frac{ -(9) \pm \sqrt{81 - 32}}{4} = \frac{-(9) \pm \sqrt{49}}{4}$$

= $$\Large \frac{-(9) \pm 7}{4} = \frac{-1}{2} , -4$$

Therefore, the required answer is

$$\Large - 4 < x < - \frac{1}{2}$$

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