Under what condition can a symmetric matrix becomes PSD

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I've just learned the concept of PSD in class, and I've got a little confusion.

If A is a symmetric matrix represented by $\pmatrix{a&b\\b&c}$, what conditions should be satisfied to becomes a PSD?

What I'm thinking is that all principle minors should be greater or equal to $0$, thus $a\ge0$, $c\ge0$, and $ac-b^2\ge0$. Is these all we need? How about $b$?

Thank you!