SOLUTION: Write a polynomial equation of least degree with roots: 1, i, and -i. Thank you so much for all of your help!!!!!! God Bless!!!!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial equation of least degree with roots: 1, i, and -i. Thank you so much for all of your help!!!!!! God Bless!!!!!!      Log On


   

Question 391971: Write a polynomial equation of least degree with roots: 1, i, and -i.
Thank you so much for all of your help!!!!!!
God Bless!!!!!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can say
x+=+1
x+=+i
x+=+-i
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Now I can say
x+-+1+=+0
x+-+i+=+0
x+-+%28-i%29+=+0
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Multiplying the left sides:
%28x+-+1%29%2A%28x+-+i%29%2A%28x+-%28-i%29%29
%28x+-+1%29%2A%28x%5E2+%2B1%29
x%5E3++%2B+x+-+x%5E2+-+1
x%5E3+-+x%5E2+%2B+x+-+1+=+0
If I substitute x+=+1, the I get
1+-+1+%2B+1+-+1+=+0 correct
and x+=+i,
-i+%2B+1+%2B+i+-+1+=+0 correct
and x+=+-i
i+%2B+1+-+i+-+1+=+0 correct
The tricky part is i%5E2+=+%28-i%29%5E2