WAEC 2023 · Paper 2 · Q2

(a)
If $3$ and $-\frac27$ are the roots of the quadratic equation $px^2 + qx + r = 0$ , find the values of $p$ , $q$ and $r$ .
Separate values with commas, e.g. 3, −2
(b)
One of the parallel sides of a trapezium is one-third the length of the other. If the height of the trapezium is $5\text{ cm}$ and its area is $120\text{ cm}^2$ , find the lengths of the parallel sides.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

If 3 and $-\frac27$ are the roots, the factors are $(x - 3)$ and $\left(x + \frac27\right)$ , or $(7x + 2)$ to avoid fractions.
$(x - 3)(7x + 2) = 7x^2 + 2x - 21x - 6$
$= 7x^2 - 19x - 6$ .
So $7x^2 - 19x - 6 = 0$ : $p = 7$ , $q = -19$ , $r = -6$ .

(b)

Let the longer parallel side be $x$ cm.
The shorter is $\frac{x}{3}$ .
Area: $\frac12\left(x + \frac{x}{3}\right) \times 5 = 120$ , so $\frac{4x}{3} \times \frac52 = 120$ , $\frac{10x}{3} = 120$ and $x = 36$ .
The parallel sides are 36 cm and 12 cm.

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