- #1

- 16

- 0

## Homework Statement

Show that the descriminant of the characteristic polynomial of

**K**is greater than 0.

[tex]K=\begin{pmatrix}-k_{01}-k_{21} & k_{12}\\

k_{21} & -k_{12}

\end{pmatrix}

[/tex]

And [itex]k_i > 0[/itex]

## Homework Equations

[tex]b^2-4ac>0[/tex]

## The Attempt at a Solution

I have tried the following:

[tex]

\begin{pmatrix}-k_{01}-k_{21}-\lambda & k_{12}\\

k_{21} & -k_{12}-\lambda

\end{pmatrix}

[/tex]

Bringing me to

[tex]\lambda^{2}+(k_{12}+k_{01}+k_{21})\lambda+k_{01}k_{12}=0[/tex]

And then plugging it into discriminant form

[tex](k_{12}+k_{01}+k_{21})^{2}-4(k_{01}k_{12})>0[/tex]

But from there I don't think that is a true statement.

Any help would be appreciated, thanks.