If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.
- \(\frac{5\sqrt{10}}{4}\)
- \(4\sqrt{10}\)
- \(5\sqrt{10}\)
-
\(\frac{4\sqrt{10}}{5}\)
The correct answer is: 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
\(5k = 4\sqrt{10} \implies k = \frac{4}{5}\sqrt{10}\)