SOLUTION: Find the zeros and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis nd turns around, at each zero. f(x)= x^3-5x^2-25x+125

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Question 1042620: Find the zeros and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis nd turns around, at each zero.
f(x)= x^3-5x^2-25x+125

Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find the zeros and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis nd turns around, at each zero.
f(x)= x^3-5x^2-25x+125
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Using synthetic division::
-5)....1....-5....-25....125
.......1...-10....25...|..0
Solve:: x^2-10x+25 = 0
(x-5)^2 = 0
Roots:: -5,5,5
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Crosses thru at x = -5
Turns around at x = 5
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Cheers,
Stan H.
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Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
f(x)= =

= = = = (x-5)*(x+5)*(x-5) = .

The roots are: 5 of multiplicity 2 and -5 of multiplicity 1.




Figure. Plot f(t) =


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