How do you solve a quadratic inequality?
- Treat it as a normal quadratic equation and solve by factorising: eg. x2 - 5x - 24 > 0 x2 - 5x - 24 = 0 (x + 3)(x - 8) = 0 x = -3 or x = 82) Sketch the curve, showing the points where the curve crosses the x-axis.3) If the sign in the inequality were to be <, the region that satisfies the inequality would be the region in between these two values (the "inside" region).But in this example, as the sign is >, the regions outside this range (the "outside" region) is the valid region.Therefore, the answer to this example question is x < -3, x > 8.As these are two different regions, we write them as two separate inequalities.4) If the question asks to shade in the valid region of the graph, we would shade in the area to the left of x = -3 and the area to the right of x = 8.
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