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

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

  • A.
    (frac{5sqrt{10}}{4})
  • B.
    (4sqrt{10})
  • C.
    (5sqrt{10})
  • D.
    (frac{4sqrt{10}}{5})
Correct Answer: Option D
Explanation

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

Expanding the right hand side equation, we have

(4x^{2} + 4xsqrt{10} + 10)

Comparing with the left hand side, we have

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