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Math Help - Repeated roots

  1. #1
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    Repeated roots

    Find all real values of k for which the equation x^4-8x^3+kx^2-8x+1 has at least one repeated root.
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  2. #2
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    You do understand that this is not a homework service nor is it a tutorial service. PLease either post some of your own work on this problem or explain what you do not understand about the question.
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  3. #3
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    First, x^2[(x+\frac{1}{x})^2-8(x+\frac{1}{x})+(k-2)]=0 where x\neq0

    Then x+\frac{1}{x} = 4 \pm \sqrt(18-k) and k= 14, -18 (rejected)

    The thing I'm not sure about is whether there are any other real values of k apart from k=14 that would give at least one repeated root...
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  4. #4
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    Quote Originally Posted by anthill View Post
    First, x^2[(x+\frac{1}{x})^2-8(x+\frac{1}{x})+(k-2)]=0 where x\neq0

    Then x+\frac{1}{x} = 4 \pm \sqrt(18-k) and k= 14, -18 (rejected)

    The thing I'm not sure about is whether there are any other real values of k apart from k=14 that would give at least one repeated root...
    I'm not sure what you are trying to do here. You seem to be assuming that x must be an integer, which is not true. If x= a, say, is a repeated root then there is a factor of (x- a)^2. Try writing x^4- 8x^3+ kx^2- 8x+ 1= (x- a)^2(x^2+ cx+ d).
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