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WAEC Further Mathematics 2017 Paper

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Question : 4

Total: 40

If

x^{2} - kx + 9 = 0

has equal roots, find the values of k.

3, 4
$\pm 3$
$\pm 5$
$\pm 6$

Solution:

Concept:

For equal roots, the discriminant of a quadratic equation must be zero.

Explanation:

Compare

x^{2} - kx + 9 = 0

with

ax^{2} + bx + c = 0

.

Here,

a = 1

,

b = -k

, and

c = 9

.

For equal roots,

b^{2} - 4ac = 0

.

Substitute the values:

(-k)^{2} - 4(1)(9) = 0

.

Simplify:

k^{2} - 36 = 0

.

So,

k^{2} = 36

.

Taking the square root gives

k = \pm 6

.

Answer:

The values of

k

are

\pm 6

, which is option D.

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