- #1

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**For which value of k does the matrix**

A=

|4 k|

|-7 -5|

have one real eigenvalue of multiplicity 2?

A=

|4 k|

|-7 -5|

have one real eigenvalue of multiplicity 2?

**3. The Attempt at a Solution**

- I tried by setting this problem up with det(A-(lambda)I) and trying to solve like that, but I can't seem to get it that way either. I am getting (lambda)^2+(lambda)-20+7k=0, but I don't know what to do from there. Please help.