Solving Polynomial Inequalities Analytically

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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Helmut Knaust
1998-06-12