# Algebra

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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 -

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 -

Based upon your explanation, I am goin to say the answer is

B(–infinity, 0) U (7, 9)

? Is this correct?

• Algebra -

Correct!

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