Determine the set of values of $k$ for which the given quadratic equation has real roots:
$2 x^{2} + k x - 4 = 0$

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Solution

$2 x^{2} + k x - 4 = 0$
Here discriminant is $D = k^{2} - 4 (- 4) (2)$
For real root $D \geq 0$
Hence $k^{2} + 32 \geq 0$
$⟹ k^{2} \geq - 32$
Hence set of values are ${k : k^{2} \geq - 32}$

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