If 4x² + 5kx + 10 is a perfect square, find the value of k.

Correct Answer is : 4105{4{10}}{5}5410

Correct Answer is : 4105{4{10}}{5}5410

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WAEC Further Mathematics 2018 Paper

Question : 5

Total: 40

4x^{2} + 5kx + 10

is a perfect square, find the value of k.

Solution:

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

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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