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WAEC Mathematics 2010 Paper

Question : 30

Total: 49

Solution:

Concept:

The roots of the equation are found by setting each factor equal to zero, and their sum is used to find the unknown constant

p

Explanation:

Given equation:

(x - p)(2x + 1) = 0

Roots occur when each factor equals zero.

So,

x - p = 0

gives the root

x = p

Also,

2x + 1 = 0

gives

x = -\frac{1}{2}

Sum of roots

= p + \left(-\frac{1}{2}\right) = p - \frac{1}{2}

It is given that the sum of roots is

1

Therefore,

p - \frac{1}{2} = 1

Add

\frac{1}{2}

to both sides:

p = 1 + \frac{1}{2} = \frac{3}{2}

Thus,

p = \frac{3}{2} = 1\frac{1}{2}

Answer:

1\frac{1}{2}

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