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Finding the domain of the square root of a polynomial

  1. Jan 4, 2008 #1
    I was just going through some problems in a maths journal for undergraduate level

    i found a sum seeming simple but i am not able to solve it completly

    find domain of [tex]\sqrt{x^{12} - x^9 + x^4 -x +1}[/tex]


    i know domain includes all negative value , all positive value >1 , but i cant get anything about (0,1)

    thanks in advance.........
     
    Last edited: Jan 4, 2008
  2. jcsd
  3. Jan 5, 2008 #2
    For [tex]x\in [0,1]\Rightarrow x-1\leq0[/tex]

    Now don't bother with the term x12, it is always positive, and factor the rest terms, i.e.

    [tex]x^{12}-x^9+x^4-x+1=x^{12}-x^4(x^5-1)-(x-1)=x^{12}+x^4(1-x^5)+(1-x)\geq0[/tex]

    as sum of non negative numbers.
     
  4. Jan 6, 2008 #3
    thanks for that....
    i was trying to do with method of intervals
     
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