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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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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graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E3-5x%5E2-25x%2B125%29
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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(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
f(x)= x%5E3-5x%5E2-25x%2B125 =

= %28x%5E3+-+5x%5E2%29+-+25%28x-5%29 = x%5E2%28x-5%29+-+25%28x-5%29 = %28x%5E2-25%29%2A%28x-5%29 = (x-5)*(x+5)*(x-5) = %28x-5%29%5E2%2A%28x%2B5%29.

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




Figure. Plot f(t) = x%5E3-5x%5E2-25x%2B125