Move all terms to one side, find the roots, then read the required intervals from a sketch. Include roots for <= or >=. For a repeated root or no real roots, use the touching or non-crossing graph. Two distinct roots: p<q, a>0 **Inequality** | **Solution** ax2+bx+c>0 | x<p or x>q ax2+bx+c >= 0 | x <= p or x >= q ax2+bx+c<0 | p<x<q ax2+bx+c <= 0 | p <= x <= q Common errors **Inequality** | **Solution** | **Take note** x2>9 | x<-3 or x>3 | Include both intervals. x2>6x | x<0 or x>6 | Do not divide by x; its sign is unknown. (x-2)(x-4)<0 | 2<x<4 | Use the sign of the product. Multiplying or dividing by a negative number reverses the inequality sign.

Move all terms to one side, find the roots, then read the required intervals from a sketch.

Include roots for \(\le\) or \(\ge\). For a repeated root or no real roots, use the touching or non-crossing graph.

Do not divide by \(x\); its sign is unknown.

Multiplying or dividing by a negative number reverses the inequality sign.

Quadratic Inequalities

Quadratic Inequalities

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