Posted by **Rachale** on Wednesday, July 22, 2009 at 11:34pm.

Solve x(x-7)(x-9)<0 and express the solution set in interval notation.

A. (–infinity, 0)

B. (–infinity, 0) U (7, 9)

C. (–infinity, 0) U (9, infinity)

D. (–infinity, 9)

- Algebra -
**MathMate**, Thursday, July 23, 2009 at 12:14am
It is a cubic, with three real zeroes (0,+7 and +9), therefore the graph crosses the x-axis three times.

The coefficicent of the x³ term is positive, so it increases to the right of the largest root (+9) and decreases to the left of the smallest root (0).

This tells us that (-∞,0) is a subset of the solution.

To find the remaining part of the solution, we note that the function is positive between 0 and the next root, and dips below zero again between the last two roots, namely +7 and +9.

Thus the missing interval is (7,9).

Can you take it from here?

- Algebra -
**Rachale**, Thursday, July 23, 2009 at 1:00am
Based upon your explanation, I am goin to say the answer is

B(–infinity, 0) U (7, 9)

? Is this correct?

- Algebra -
**MathMate**, Thursday, July 23, 2009 at 7:16am
Correct!

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