SOLUTION: Eh...I'm not sure where this one would be catogorized. I'm really sorry! I really need help though, please... Find the zero's of: {{{P(x)=x^3-5x^2+16x-80}}}

Algebra ->  Square-cubic-other-roots -> SOLUTION: Eh...I'm not sure where this one would be catogorized. I'm really sorry! I really need help though, please... Find the zero's of: {{{P(x)=x^3-5x^2+16x-80}}}      Log On


   

Question 143275: Eh...I'm not sure where this one would be catogorized. I'm really sorry! I really need help though, please...
Find the zero's of:
P%28x%29=x%5E3-5x%5E2%2B16x-80
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=x%5E3-5x%5E2%2B16x-80 Start with the given function


0=x%5E3-5x%5E2%2B16x-80 Plug in P%28x%29=0


0=%28x%5E3-5x%5E2%29%2B%2816x-80%29 Group like terms


0=x%5E2%28x-5%29%2B16%28x-5%29 Factor out the GCF x%5E2 out of the first group. Factor out the GCF 16 out of the second group


0=%28x%5E2%2B16%29%28x-5%29 Since we have the common term x-5, we can combine like terms



Now set each factor equal to zero:

x%5E2%2B16=0 or x-5=0

Now solve for x for each factor:

x%5E2=-16 or x=5


x=0%2B-sqrt%28-16%29 or x=5


Take the square root of -16 to get 4i and -4i

x=4i, x=-4i, or x=5



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Answer:
So our answers are


x=4i, x=-4i, or x=5