SOLUTION: Given: {{{P(x)=x^3-3x^2+25x-75}}} Find all zeros real and imaginary.

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Question 165612: Given:
P%28x%29=x%5E3-3x%5E2%2B25x-75
Find all zeros real and imaginary.
Answer by oscargut(686) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=x%5E3-3x%5E2%2B25x-75=x%5E2%2A%28x-3%29%2B25%2A%28x-3%29=%28x%5E2%2B25%29%2A%28x-3%29=0
then

x%5E2%2B25=0 or x-3=0
then
x^2=-25 then x=5i or -5i
x-3=0 then x=3
Answer:
zeros are: 5i,-5i,3