JAMB Mathematics 2023 Paper

Concept:Quadratic inequalities are solved by writing them in standard form, factoring to find boundary values, and testing intervals on the number line.Explanation:Start with the given inequality: $x^2 - x - 4 \le 2$.Subtract $2$ from both sides to get the standard form:$x^2 - x - 4 - 2 \le 0$$x^2 - x - 6 \le 0$Factor the left side:$(x - 3)(x + 2)\le 0$Set each factor equal to zero to find the boundary points:$x - 3 = 0$ gives $x = 3$$x + 2 = 0$ gives $x = -2$These values split the number line into three intervals.Test a point between $-2$ and $3$, for example $x = 0$:$(0 - 3)(0 + 2) = (-3)(2) = -6$Since $-6 \le 0$ is true, the inequality is satisfied between $-2$ and $3$.Because the inequality includes $\le$, the endpoints are also included.Answer:B. $-2 \le x \le 3$