JAMB Mathematics 2015 Paper

Concept:Turn the word problem into a quadratic equation using the sum and product, then solve it.Explanation:Let the first number be $x$. Since the sum of the two numbers is $5$, the second number is $5 - x$.The product is $-14$, so we form the equation:$$x(5 - x) = -14$$Expanding: $5x - x^2 = -14$.Rearrange into the standard quadratic form:$$x^2 - 5x - 14 = 0$$Factorise the quadratic:$$(x - 7)(x + 2) = 0$$Set each factor to zero and solve:$x - 7 = 0$, giving $x = 7$$x + 2 = 0$, giving $x = -2$Check: $7 + (-2) = 5$, and $7 \times (-2) = -14$.Both conditions are satisfied.Answer:The numbers are $7$ and $-2$, so $x = 7$ or $x = -2$.