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Finding x for a certain quadratic form

  1. Apr 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose a,c>0 and [itex]b^2-4ac>0 [/itex]. Explain how you could find [itex] x_1, x_2 ε ℝ [/itex]
    such that [itex]a(x_1) ^2+bx_1x_2+c(x_2)^2<0 [/itex].


    2. Relevant equations
    [tex]q\begin{pmatrix}x_1\\x_2\end{pmatrix} = a(x_1)^2+bx_1x_2+c(x_2)^2[/tex]


    3. The attempt at a solution
    I'm not sure where to go with this. This is part (b) of a question and my answer for part (a) shows that q takes both positive and negative values. I also know this equation can be changed into a real symmetric matrix. Maybe I can use that or have q( x1 x2 ) equal the symmetric matrix?
     
  2. jcsd
  3. Apr 12, 2013 #2
    I think I've solved it. It involves setting up the equation q( x1 x2 x3) = [x1 x2 x3] * A * (x1 x2)
     
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