WAEC 2023 · Paper 1 · Q8

If $\alpha$ and $\beta$ are the roots of $7x^2 + 12x - 4 = 0$ , find the value of $\dfrac{\alpha\beta}{(\alpha + \beta)^2}$ .

Worked solution (try it first)

For $ax^2 + bx + c = 0$ , the sum of the roots is $-\frac{b}{a} = -\frac{12}{7}$ and the product is $\frac{c}{a} = -\frac{4}{7}$ .
Square the sum: $(\alpha + \beta)^2 = \frac{144}{49}$ .
Divide: $-\frac{4}{7} \times \frac{49}{144} = -\frac{196}{1008}$
$= -\frac{7}{36}$ , option C.