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Perfect square

  1. Apr 10, 2008 #1
    1. The problem statement, all variables and given/known data

    If the polynomial P(x)=x^4+ax^3+bx^2-8x+1 is a perfect square then find (a+b)

    3. The attempt at a solution
    The first term is a perfect square and so is the last term. that means that th middle terms should have been =2x^2.
    But it is not so, then how can this be a perfect square?
     
  2. jcsd
  3. Apr 10, 2008 #2

    HallsofIvy

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    P(x) is a perfect square of what? Since it involves x4, it must be the square of a quadratic. What is (x^2+ ux+ 1)2? What values of a, b, and u make those the same?
     
    Last edited: Apr 11, 2008
  4. Apr 11, 2008 #3


    Thanks. I have solved the problem. But will you please tell me how did you figure out that the skeleton expression given was the square of a trinomial?
     
  5. Apr 11, 2008 #4

    HallsofIvy

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    I didn't "figure" that out. The given expression involved x4 so I knew it must be the square of a quadratic. The most general quadratic is ax2+ bx+ c. Then I saw that, in order to get "x4" and "+ 1" I must have a= 1, c= 1. I still did not know what b was so I left that in. I did not know that b was not 0, just that there was no reason to assume it wasn't!
     
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