Question

The solution set of x(x-5) is greater than or equal to 0 is

Answer 1

Solve x(x-5)=0; the roots are 0 and 5.

Draw a number line. Plot 0 and 5 on this line.
Set up 3 intervals, as follows: (-infinity, 0), (0, 5), and (5, infinity).

Now choose a test number from within each interval (e. g., -2, 3, 10).

Subst. each into the inequality x(x-5)
`\geq` 0. In each case, determine whether the inequality is true or false.

Based upon your results here, you should be able to determine on which interval or intervals the inequality is true. Those interval(s) is/are your solution set.