WAEC Mathematics 2023 Paper

Concept:Factorise the quadratic expression by splitting the middle term, then set each factor equal to zero to find the roots.Explanation:Given equation: $3m^2 - 2m - 65 = 0$Find two numbers whose product is $3 \times (-65) = -195$ and whose sum is $-2$.These numbers are $-15$ and $13$.Rewrite the middle term: $3m^2 - 15m + 13m - 65 = 0$Group terms: $3m(m - 5) + 13(m - 5) = 0$Factor out $(m - 5)$: $(m - 5)(3m + 13) = 0$Now solve each factor: $m - 5 = 0$ gives $m = 5$And $3m + 13 = 0$ gives $m = \frac{-13}{3}$Thus, the roots are $5$ and $\frac{-13}{3}$.Answer:The roots are $\left(5, \frac{-13}{3}\right)$, so the correct option is B.