SOLUTION: Given -5i is a root determine all other roots of f(x)=x^3+5x^2+25x+125

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Question 732062: Given -5i is a root determine all other roots of f(x)=x^3+5x^2+25x+125
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3%2B5x%5E2%2B25x%2B125...factor completely
set f%28x%29=0
0=%28x%5E3%2B5x%5E2%29%2B%2825x%2B125%29

x%5E2%28x%2B5%29%2B25%28x%2B5%29=0

%28x%5E2%2B25%29%28x%2B5%29=0

if %28x%5E2%2B25%29=0...=>...x%5E2=-25..=>...x=sqrt%28-25%29..=>...x=5i or x=-5i
if x%2B5=0..=>...x=-5

so, roots are:
x=-5...real
x=5i.......complex
x=-5i......complex

+graph%28+600%2C+600%2C+-10%2C+10%2C+-50%2C+150%2Cx%5E3%2B5x%5E2%2B25x%2B125%29+