How does a concave function lead to cconvex inequalities?

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I came across this in page 360 of Boyd Vandenbergh's book on Convex Optimisation:

ad to convex inequalities?

What is the meaing of the statement:

It follows that a lower bound on the variance of $X$ can be expressed as a convex quadratic inequality on $p$

and how does it follow, it seems pretty unclear to me.