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## Homework Statement

I need to diagonalize the matrix A=

1 2 3

2 5 7

3 7 11

## The Attempt at a Solution

Subtracting λI and taking the determinant, the characteristic polynomial is

λ

^{3}- 17λ

^{2}+ 9λ - 1 (I have checked this over and over)

The problem now is it has some ugly roots, none that I would never be able to find without a calculator (which is sort of the objective here). Anyways, is there some other way to find P such that

P

^{-1}AP = P

^{T}AP is a diagonal matrix?

*edit* I would just add that the matrix A is the matrix associated to the quadratic form q(v) = x

^{2}+ 5y

^{2}+ 11z

^{2}+ 4xy + 6xz + 14yz

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