If $p$ is a prime where $p=4k+3$ and $a$ is a quadratic residue modulo $p$, then exactly one if its roots is a QR modulo $p$?

Question

I recall encountering a theorem which stated something like: if $p$ is a prime of the form $p=4k+3$ and $a$ is a quadratic residue (QR) modulo $p$, then exactly one if its roots is a QR modulo $p$.

I tried proving this to myself using the fact that $a^{\frac{p-1}{2}}=1$ (because it's a QR), which leads to $a^{k+1}$ being one of $a$'s roots, but I can't see how to proceed from here. Assuming this statement is correct, how can I complete the proof? (or, is there a resource I can refer to?).

Thanks.