Correct Answer: Option D

Explanation

\(4x^{2} + 5kx + 10 = (2x + \sqrt{10})^{2}\)

Expanding the right hand side equation, we have

\(4x^{2} + 4x\sqrt{10} + 10\)

Comparing with the left hand side, we have

\(5k = 4\sqrt{10}  \implies k = \frac{4}{5}\sqrt{10}\)

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