JAMB Mathematics 2019 Paper

Concept:A quadratic inequality is solved by factoring, then determining the interval where the product of the factors satisfies the inequality sign.Explanation:Factor the quadratic expression: $x^2 - 7x + 10 = (x-5)(x-2)$.Thus, the inequality becomes $(x-5)(x-2) \leq 0$.A product is non-positive when the two factors have opposite signs or one factor is zero.The critical points are $x = 2$ and $x = 5$, where each factor becomes zero.Test a value between the critical points, such as $x = 3$: $(3-5)(3-2) = (-2)(1) = -2 \leq 0$.This satisfies the inequality, so the solution lies between $2$ and $5$.For values like $x < 2$ or $x > 5$, the product becomes positive, which does not satisfy the inequality.Therefore, $x$ must be at least $2$ and at most $5$.Answer:$\boldsymbol{2 \leq x \leq 5}$The correct option is D.