Finding Eigenvalues (with a variable)

So I have the matrix

$\displaystyle A=\left(\begin{matrix} 2/5 &1/5\\x &0\end{matrix}\right)$

And it asks me to find the eigenvalues (as expressions in the parameter x)

So using λ=Lambda I got: λ^2-(2/5)λ-(1/5)x. How am I supposed to factor that to find the eigenvalues when x is there?

Re: Finding Eigenvalues (with a variable)

Quote:

Originally Posted by

**calculuskid1** So using λ=Lambda I got: λ^2-(2/5)λ-(1/5)x. How am I supposed to factor that to find the eigenvalues when x is there?

Solving the quadratic equation $\displaystyle \lambda^2-(2/5)\lambda -(1/5)x=0$ you'll obtain $\displaystyle \lambda=\frac{1\pm \sqrt{1+5x}}{5}$ .

Re: Finding Eigenvalues (with a variable)

Thank you! I'm not sure why I didn't think to use the quadratic formula! I always forget to go back to basic principles lol