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:

Concept:

A quadratic expression is a perfect square if it can be written as the square of a linear binomial.

Explanation:

Let

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

Expanding,

(2x + a)^{2} = 4x^{2} + 4ax + a^{2}

Comparing constants:

a^{2} = 10

, so

a = \sqrt{10}

Comparing the coefficient of

x

5k = 4a = 4\sqrt{10}

Therefore,

k = \frac{4\sqrt{10}}{5}

Answer:

k = \frac{4\sqrt{10}}{5}

, which is option D.

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