WAEC Further Mathematics 2025 Paper

Concept:Factor the quadratic expression, locate the boundary points, and test intervals to find where the product is non-negative.Explanation:We need to solve $2x^2 + 5x - 3 \geq 0$.Factor the quadratic:$2x^2 + 5x - 3 = (2x - 1)(x + 3)$.So the inequality becomes:$(2x - 1)(x + 3) \geq 0$.The critical points are found by setting each factor to zero:$2x - 1 = 0 \Rightarrow x = \frac{1}{2}$$x + 3 = 0 \Rightarrow x = -3$.Now test the intervals:For $x \leq -3$, both factors are non-positive, so the product is non-negative.For $-3 \leq x \leq \frac{1}{2}$, the product is negative.For $x \geq \frac{1}{2}$, both factors are non-negative, so the product is non-negative.Therefore, the solution set is:$x \leq -3$ or $x \geq \frac{1}{2}$.Answer:Option C: $x \leq -3$ or $x \geq \frac{1}{2}$.