SOLUTION: the question states given -5i is a root, determine all other roots f(x)=

Algebra ->  Equations -> SOLUTION: the question states given -5i is a root, determine all other roots f(x)=      Log On


   

Question 681837: the question states given -5i is a root, determine all other roots f(x)=
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
x = -5i
There will also be +5i as the conjugate pair
...
x%5E2+=+%285i%29%5E2
...
x%5E2+=+25i%5E2
where i%5E2+=+sqrt%28-1%29%5E2+=+-1
...
x%5E2+=+25%28-1%29
..
x%5E2+=+-25
x%5E2+%2B+25+=+0
...
%28x%5E3%2B5x%5E2%2B25x%2B125%29%2F%28x%5E2%2B25%29
...
x%5E2%2B25%29+goes+into+%7B%7B%7Bx%5E3+%2B5x%5E2: x
to get
x%5E3+%2B+25x
subtracting
x%5E3+-+x%5E3+%2B+5x%5E2+-+25x
yielding
5x%5E2+-+25x
...
x%5E2%2B25 goes into 5x%5E2-25x%2B25x: 5
to get
5x%5E2%2B125
subtracting
5x%5E2+-+5x%5E2+-+125
yielding
-125
...
x%5E2%2B25 goes into -125%2B125: 0
...
%28x%5E3%2B5x%5E2%2B25x%2B125%29%2F%28x%5E2%2B25%29+=+%28x%2B5%29
Therefore, the factors are
%28x%5E2%2B25%29%28x%2B5%29=0
………………………
Do you have more questions?
Email: HomeworkHelpers@ReadingBoosters.com
Delighted to help!
-Reading Boosters
Website: www.MyHomeworkAnswers.com