If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.

  • A \(\frac{5\sqrt{10}}{4}\)
  • B \(4\sqrt{10}\)
  • C \(5\sqrt{10}\)
  • D \(\frac{4\sqrt{10}}{5}\)
waec 2018furthermathematics

The correct answer is D. \(\frac{4\sqrt{10}}{5}\)

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

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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