Quadratic Functions, Equations and Inequalities - Quadratic Inequalities

Quadratic Functions, Equations and Inequalities - Quadratic Inequalities

TGM Original Questions

Find the range of values of \(x\) for which

\({{x}^{2}}-12x+9>0\)
\({{x}^{2}}-12x\le 0\)

Hence solve the inequality \(-9<{{x}^{2}}-12x\le 0\).

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Answer:(a) \(x<6-3\sqrt3\) or \(x>6+3\sqrt3\) (b) \(0\leq x\leq12\) Hence \(0\leq x<6-3\sqrt3\) or \(6+3\sqrt3<x\leq12\)

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