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WAEC Further Mathematics 2014 Paper

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Question : 31

Total: 40

For what values of m is

9y^{2} + my + 4

a perfect square?

$\pm 2$
$\pm 3$
$\pm 6$
$+12$

Solution:

Concept:

A quadratic expression is a perfect square if it can be written in the form

(ay \pm b)^2

.

Explanation:

Compare

9y^2 + my + 4

with

(3y \pm 2)^2

.

First expand

(3y + 2)^2

:

(3y + 2)^2 = 9y^2 + 12y + 4

.

This gives

m = +12

.

Now expand

(3y - 2)^2

:

(3y - 2)^2 = 9y^2 - 12y + 4

.

This gives

m = -12

.

So both positive and negative values make the expression a perfect square.

Answer:

m = \pm 12

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