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Roots of a squared polynomial ( complex numbers)

  1. Apr 3, 2014 #1
    1. The problem statement, all variables and given/known data

    problem in a pic attached

    2. Relevant equations



    3. The attempt at a solution
    i solved i and ii a , when it came to b , i just said that every one of the 3 roots will be squared having 2 roots 1 + and 1 - but then i read the marking schemes ( also attached) , and i got really confused and now i dont know what he wants from me
     
  2. jcsd
  3. Apr 3, 2014 #2

    Ray Vickson

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    He wants you to tell him what are all the square roots of -2, -2+2*sqrt(3)*i and -2 - 2*sqrt(3)*i.
     
  4. Apr 3, 2014 #3
    why cant i just say (z+2)^2= 0 and solve and do the same for the complex roots?
    why do i have to find the roots of the -2?
     
  5. Apr 3, 2014 #4
    (z + 2)2 is not a factor of p(z2). It is a factor of (p(z))2, however, a completely different polynomial.
    The polynomial is not the object being squared. p(z2) only means that the variable z is being replaced with the variable z2. So, as a result, we know that z2 + 2 is a factor.
     
  6. Apr 3, 2014 #5
    okay...thanks very much, tht was a tricky one, or maybe i am stupid :D
    either way , thanks , i got it
     
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