# Finding Eigenvalues (with a variable)

• October 1st 2011, 09:38 AM
calculuskid1
Finding Eigenvalues (with a variable)
So I have the matrix
$A=\left(\begin{matrix} 2/5 &1/5\\x &0\end{matrix}\right)$
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?
• October 1st 2011, 09:51 AM
FernandoRevilla
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 $\lambda^2-(2/5)\lambda -(1/5)x=0$ you'll obtain $\lambda=\frac{1\pm \sqrt{1+5x}}{5}$ .
• October 1st 2011, 10:07 AM
calculuskid1
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