WAEC Further Mathematics 2011 Paper

Concept:A quadratic inequality can be solved by factorising the expression and testing the intervals between the critical points.Explanation:Factorise the quadratic expression.$3x^{2} + 4x + 1 = 3x^{2} + 3x + x + 1$$= 3x(x + 1) + 1(x + 1)$$= (3x + 1)(x + 1)$So the inequality becomes:$(3x + 1)(x + 1) > 0$Set each factor equal to zero to find the critical points.$3x + 1 = 0 \implies x = -\frac{1}{3}$$x + 1 = 0 \implies x = -1$Test the intervals created by these points.For $x < -1$, both factors are negative, so the product is positive.For $-1 < x < -\frac{1}{3}$, one factor is positive and the other is negative, so the product is negative.For $x > -\frac{1}{3}$, both factors are positive, so the product is positive.Therefore, the inequality is satisfied when $x < -1$ or $x > -\frac{1}{3}$.Answer:$x < -1$ or $x > -\frac{1}{3}$