YuLM20080807-1

From 高材生

$\begin{align} & f\left( x \right)=ax^{2}-3ax-1+a \\ & f\left( x \right)=a\left( x^{2}-2\times \frac{3}{2}x+\left( \frac{3}{2} \right)^{2} \right)-a\left( \frac{3}{2} \right)^{2}-1+a \\ & =a\left( x-\frac{3}{2} \right)^{2}-\frac{5a+4}{4} \\ & f\left( x \right)<0\Rightarrow a\left( x-\frac{3}{2} \right)^{2}-\frac{5a+4}{4}<0 \\ & a=0\Rightarrow f\left( x \right)=-1 \\ & \left\{ \begin{align} & a<0 \\ & \frac{5a+4}{4}>0\Rightarrow 5a>-4\Rightarrow a>-0.8 \\ \end{align} \right. \\ & \therefore -0.8<a<0 \\ & f\left( x \right)<0\Rightarrow -0.8<a\le 0 \\ & f\left( x \right)>0\Rightarrow a\left( x-\frac{3}{2} \right)^{2}-\frac{5a+4}{4}>0 \\ & \left\{ \begin{align} & a>0 \\ & \frac{5a+4}{4}<0\Rightarrow 5a+4<0\Rightarrow a<-0.8 \\ \end{align} \right. \\ \end{align}$

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YuLM20080807-1

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