Eigenvalues[({{ea, λ}, {λ, ea}})]

Eigenvalues[({{ea, λ(Sqrt[2]), 0}, {λ(Sqrt[2]), eb, λ(Sqrt[2])}, {0, λ(Sqrt[2]), ea}})]//FullSimplify

Eigenvalues[({{ea, λ(Sqrt[3]), 0, 0}, {λ(Sqrt[3]), eb, 2λ, 0}, {0, 2λ, eb, λ(Sqrt[3])}, {0, 0, λ(Sqrt[3]), ea}})]//FullSimplify

Eigenvalues[({{100, λ}, {λ, 100}})]

Plot[{100-λ,100+λ}, {λ,0,5}]

Eigenvalues[({{100, λ(Sqrt[2]), 0}, {λ(Sqrt[2]), 105, λ(Sqrt[2])}, {0, λ(Sqrt[2]), 100}})]

Plot[{100,(1/2) (205-(Sqrt[25+16 (λ^2)])),(1/2) (205+(Sqrt[25+16 (λ^2)]))}, {λ,0,5}]

Eigenvalues[({{100, λ(Sqrt[3]), 0, 0}, {λ(Sqrt[3]), 105, 2λ, 0}, {0, 2λ, 105, λ(Sqrt[3])}, {0, 0, λ(Sqrt[3]), 100}})]

Plot[{(1/2) (205-2 λ-(Sqrt[25-20 λ+16 (λ^2)])),(1/2) (205-2 λ+(Sqrt[25-20 λ+16 (λ^2)])),(1/2) (205+2 λ-(Sqrt[25+20 λ+16 (λ^2)])),(1/2) (205+2 λ+(Sqrt[25+20 λ+16 (λ^2)]))}, {λ,0,5}]