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Finding Polynomials

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a polynomial with integer coefficient for which [tex]\sqrt(2) + i[/tex] is a zero.

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?
     
  2. jcsd
  3. Apr 19, 2009 #2
    consider (sqrt(2)+i)2...what are you left with after expanding and simplifying?
    how about (sqrt(2)+i)4?
     
  4. Apr 23, 2009 #3
    Ok, as an answer I got:

    [tex]x^2 - 2 \sqrt{2}x + 2 - i[/tex]
    Does that look right?
     
  5. Apr 23, 2009 #4
    Latex isn't working, so I got

    x^2 - 2sqrt(2)x + 2 - i
     
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