checkccompilers returns "Compiler test failed" and "Could not compile test" error

Symptoms

/usr/local/cpanel/scripts/checkccompilers returns errors like these:

Compiler test failed.  Attempting to autorepair compiler.

and

Could not compile test

When the script runs as part of upcp, it generates an error like this, which the system also sends via email:

The “/usr/local/cpanel/scripts/checkccompiler” command (process 627338) reported error number 1 when it ended.

This error can appear if there is an issue with the glibc RPMs installed on the server.

Have your system administrator or data center verify the integrity of the glibc packages and reinstall the affected one(s).