WAEC Further Mathematics 2024 Paper

Concept:Solving a quadratic inequality by rearranging, factorising, and testing the sign intervals.Explanation:Start with the given inequality:$$9x - 1 > 14x^2$$Bring all terms to one side:$$14x^2 - 9x + 1 < 0$$Factorise the quadratic expression:$$14x^2 - 9x + 1 = (7x - 1)(2x - 1)$$So the inequality becomes:$$(7x - 1)(2x - 1) < 0$$Find the critical values:$$7x - 1 = 0 \Rightarrow x = \frac{1}{7}$$$$2x - 1 = 0 \Rightarrow x = \frac{1}{2}$$The coefficient of $x^2$ is positive, so the parabola opens upward.Therefore, the product is negative between the two roots:$$\frac{1}{7} < x < \frac{1}{2}$$Testing a value such as $x = 0.3$ confirms the inequality holds in this interval.Answer:$$\frac{1}{7} < x < \frac{1}{2}$$Option A.