While there is no native way in Windows 10 (yet) to change Cortana to query Google instead of Bing to get you the answers she searches for, there are plugins for Google Chrome that achieve the same results provided that you use Chrome as your default web browser.
Set Chrome as your Default Browser in Windows Store (video here how to do it) and then you can install Bing2Google Chrome Extension. Then whenever you ask Cortana to search for something it queries Bing but immediately redirects that same query to Google and you end up with a Google search result answer.
Same concept except Chrometana can support DuckDuckGo and other search engines and works without Chrome even being open if you have background apps enabled. In order for Chrometana to work when Chrome is closed, you must have background apps enabled. If you have disabled background apps, you can re-enable by doing the following:
1. Go toChrome Settings
2. Click “Show Advanced Settings”
3. Scroll down to System
4. Check “Continue running background apps when Google Chrome is closed”