NECO 2024 · Paper 1 · Q31

Find the roots of the equation $8x^2 - 6x - 9 = 0$ .

Worked solution (try it first)

Find two numbers with product $8 \times (-9) = -72$ and sum $-6$ : they are $-12$ and 6.
Split and group: $8x^2 - 12x + 6x - 9 = 4x(2x - 3) + 3(2x - 3)$
$= (2x - 3)(4x + 3)$ .
Set each factor to zero: $2x - 3 = 0$ gives $x = \frac32$ and $4x + 3 = 0$ gives $x = -\frac34$ , option B.