SOLUTION: How can you solve the polynomial inequality {{{z^3-6z^2+9z<0}}}?

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Question 118335: How can you solve the polynomial inequality z%5E3-6z%5E2%2B9z%3C0?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve the polynomial inequality z^3-6z^2+9z<0
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Factor the left side:
z(z^2-6z+9) < 0
z(z-3)^2 < 0
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Draw a number line.
Mark the points z=0 and z=3.
Check a test point in each of the three resulting intervals:
Interval (-inf,0); Let z=-1, you get (-1)(-1-3)^2<0 which is true
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Interval (0,3); Let z=1, you get (1)(1-3)^2<0 which is false
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Interval (3,+inf); Let=4 you get (4)(4-3)^2<0 which is false
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Solution:
z < 0
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Cheers,
Stan H.