Quadratic Functions, Equations and Inequalities - Equations Reducible to Quadratics
Quadratic Functions, Equations and Inequalities - Equations Reducible to Quadratics
IP 3
- Find \(\mathrm{Q}\left( x \right)\) if \({{x}^{4}}-6{{x}^{3}}+6{{x}^{2}}+7x+3=\left( {{x}^{2}}-5x+3 \right)\mathrm{Q}\left( x \right)+9\).
- Solve \({{x}^{4}}-6{{x}^{3}}+6{{x}^{2}}+7x-6=0\). Hence sketch the curve \(y={{x}^{4}}-6{{x}^{3}}+6{{x}^{2}}+7x-6\) and state the range of values of \(x\) such that
- \(y>0\),
- \(\frac{1}{y}<0\).
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Answer:(a) \(Q(x)=x^2-x-2\) (b) \(x=-1,\ \frac{5-\sqrt{13}}{2},\ 2,\ \frac{5+\sqrt{13}}{2}\) (i) \(x<-1\), \(\frac{5-\sqrt{13}}{2}<x<2\), or \(x>\frac{5+\sqrt{13}}{2}\) (ii) \(-1<x<\frac{5-\sqrt{13}}{2}\) or \(2<x<\frac{5+\sqrt{13}}{2}\)
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