# Finding x for a certain quadratic form

1. Apr 12, 2013

### vellum93

1. The problem statement, all variables and given/known data

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

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

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. Apr 12, 2013

### vellum93

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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