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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

Correct Answer:

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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