linear algebra - Positive diagonal entries in $2 times 2$ matrix

I am facing the following problem:

A symmetric $2 \times 2$ matrix $A$ has eigenvalues $\lambda_1 = 3$ and $\lambda_2 = 4$. Compute the determinant and trace of $A$. Is the following statement true, false or depends on the particular entries of $A$?

"All diagonal entries of $A$ are positive."

I know that $\det(A) = 12$ and $\mbox{tr}(A) = 7$. How can I determine the signs of the diagonal entries?