Finding Eigenvalues for a Matrix with One Real Eigenvalue of Multiplicity 2

[jmcasall]

For which value of does the matrix
-4 k
-3 -7


have one real eigenvalue of multiplicity 2??

I use det(µI-A)=0
and end up with µ^2 - 3µ - 28 + 3k
but i don't know where to go from here
pls help

 

[ice109]

think

 

[jmcasall]

haha thanks

 

[ircdan]

For which value of does the matrix
-4 k
-3 -7


have one real eigenvalue of multiplicity 2??

I use det(µI-A)=0
and end up with µ^2 - 3µ - 28 + 3k
but i don't know where to go from here
pls help

you sure you computed the determinant correctly?

anyways after you correct it, hint: quadratic formula

 

[ice109]

yea you did do it wrong... do it again and then think

 

[HallsofIvy]

In particular, after you have the correct equation, think about the discriminant of the equation.

 

[jmcasall]

thanks
your help has been greatly appreciated