For real values of $x$ , $2 x^{2} + 5 x - 3 > 0$ , if-

x < - 2

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x > 0

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x \in (- \infty, - 3) U (\frac{1}{2}, \infty)

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none of these

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Solution

The correct option is C $x \in (- \infty, - 3) U (\frac{1}{2}, \infty)$
${2 x}^{2} + 5 x - 3 > 0 {2 x}^{2} + 6 x - x - 3 > 0 2 x (x + 3) - 1 (x + 3) > 0 (x + 3) (x - \frac{1}{2}) > 0 ∴ x \in (- \infty, - 3) U (\frac{1}{2}, \infty)$

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