I took a 1 mg zanax on the 20th and 21st and have a laboratory drug screen on the 05th. Since its going to be 2 weeks since last use and I'm not a active user to the medicine would it still be detected?

Depends on half life. The half life of a drug is how long it takes for the concentration of it in your blood stream to fall to 50% of the maximum (which is right after u take the drug). Generally, they say 5 half-lives are needed to get rid of the drug. For Xanax, (alprazolam) the half-life is about 11.2 hrs, though it can range from 6 hrs to 24 hrs depending on ur specific condition, genetics, & other meds/foods u may ingest.