SOLUTION: Just a little more help. Find the zeros of the polynomial function: F(x)=x³-6x²+9x Thanks again

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Just a little more help. Find the zeros of the polynomial function: F(x)=x³-6x²+9x Thanks again      Log On


   

Question 134216: Just a little more help.
Find the zeros of the polynomial function:
F(x)=x³-6x²+9x
Thanks again
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3-6x%5E2%2B9x Start with the given equation


0=x%5E3-6x%5E2%2B9x Set f(x) equal to zero


0=x%28x%5E2-6x%2B9%29 Factor out an "x"


0=x%28x-3%29%28x-3%29 Factor x%5E2-6x%2B9 to get %28x-3%29%28x-3%29 (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x=0, x-3=0 or x-3=0

x=0, x=3 or x=3 Now solve for x in each case



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Answer:

So our solutions are

x=0 or x=3




Notice if we graph y=x%5E3-6x%5E2%2B9x we can see that the roots are x=0 and x=3 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E3-6x%5E2%2B9x%29+