Solving Polynomial Inequalities Analytically

Exercise 1.

Find the solutions of the inequality

\begin{displaymath}2-x^2\geq 0.\end{displaymath}


The roots of the equation 2-x2=0 are $x=\pm\sqrt{2}$, leading to the following picture:

The set of solutions of the inequality is the interval $(-\sqrt{2},\sqrt{2})$.

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