Solving Polynomial Inequalities Analytically

Exercise 5.

Find the solutions of the inequality

$\begin{displaymath}x^3\geq x^2.\end{displaymath}$

Answer.

Rewrite as $x^3-x^2 \geq 0$ . The roots of the corresponding equation are x=0 and x=1.

The tricky part is reading off all solutions: Clearly, the numbers in the interval $[1,\infty)$ are solutions, but don't forget x=0. (Check that x=0 is indeed a solution!) Thus the set of solutions is the following set:

$\begin{displaymath}\{0\}\cup [1,\infty).\end{displaymath}$

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Helmut Knaust
1998-06-12