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})