Add test to demonstrate bug

tests/test_root_path_redirects.py

@@ -0,0 +1,36 @@
+from fastapi import APIRouter, FastAPI
+from fastapi.testclient import TestClient
+
+
+def test_redirects_without_root_path():
+    app = FastAPI()
+    router = APIRouter()
+
+    @router.get("/hello/")
+    def hello_page() -> str:
+        return "Hello, World!"
+
+    app.include_router(router)
+
+    client = TestClient(app, base_url="http://testserver")
+
+    response = client.get("/hello", follow_redirects=False)
+    assert response.status_code == 307
+    assert response.headers["location"] == "http://testserver/hello/"
+
+
+def test_redirects_with_root_path():
+    app = FastAPI(root_path="/api")
+    router = APIRouter()
+
+    @router.get("/hello/")
+    def hello_page() -> str:
+        return "Hello, World!"
+
+    app.include_router(router)
+
+    client = TestClient(app, base_url="http://testserver")
+
+    response = client.get("/hello", follow_redirects=False)
+    assert response.status_code == 307
+    assert response.headers["location"] == "http://testserver/api/hello/"