Ononot — For a 2 \times 2 matrix A = \begin{pmatrix} a & b \\ c & d \

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Eigenvalues & Eigenvectorseasy

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For a $2 \times 2$ matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ , the characteristic polynomial is given by $p(\lambda) = \lambda^2 - \text{tr}(A)\lambda + \det(A)$ . If $\text{tr}(A) = 4$ and $\det(A) = 3$ , what is $p(\lambda)$ ?