WAEC Further Mathematics 2023 Paper

The general form of a quadratic equation is:

$x^2$ -(sum of roots)$x$ +(product of roots) = 0

$7x^2+12x-4=0$

Divide through by 7

=$x^2 + \frac{12}{7}x - \frac{4}{7} = 0$

=$x^2 - \left(-\frac{12}{7}\right)x + \left(-\frac{4}{7}\right) = 0$

$\therefore$ sum of roots = $-\frac{12}{7}$, and products of roots =$-\frac{4}{7}$

α + β = $-\frac{12}{7}, \alpha\beta = -\frac{4}{7}$

$\frac{\alpha\beta}{(\alpha + \beta)^2} = \frac{-\frac{4}{7}}{\left(-\frac{12}{7}\right)^2}$

=$\frac{-\frac{4}{7}}{\frac{144}{49}} = -\frac{4}{7} \times \frac{49}{144}$

$\therefore -\frac{7}{36}$