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For how many integers $x$ is the number $x^{4}-7x^{2}+12$ negative? (  2014 AMC 10B Problems, Question \#20) 
Overseas Competition->Knowledge Point->Calculation Modules
Factor the polynomial as $\left(x^{2}-4\right)\left(x^{2}-3\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-4\textless0\textless x^{2}-3$. Solving this inequality, we find $3\textless x^{2}\textless4$. There is no integer $x$ that satisfies this inequality. 