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Larger eigenvalue of a 2×2

MediumLinear Algebra~3m

What is the larger eigenvalue of (5222)\begin{pmatrix}5&2\\2&2\end{pmatrix}?

Show hints (2)+
  1. Eigenvalues solve λ2−(tr⁡)λ+det⁡=0\lambda^2-(\operatorname{tr})\lambda+\det=0.
  2. λ2−7λ+6=0\lambda^2-7\lambda+6=0.

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