You can accomplish this in multiple ways, the easiest way is to use a *Hair Info* node, and use the *Intercept* value to drive a *Converter > Color Ramp* node. Use this to drive the *Factor* on your mix or add shader node. Here is a quick example node setup:
![enter image description here][1]

And here is how it renders:
![enter image description here][2]

As you can see, the lower input into the *Mix Shader* is on the base of the hair, and the upper input is on the top of the hair. This will work on a *Color > Mix RGB* node as well.

EDIT: It is also possible to add another set of colors on top of the first two, giving even more controlability:
![enter image description here][3]

How it renders:
![enter image description here][4]

More realistic colorings:
![enter image description here][5]


  [1]: https://i.sstatic.net/hlHII.png
  [2]: https://i.sstatic.net/2O98e.png
  [3]: https://i.sstatic.net/M1BQq.png
  [4]: https://i.sstatic.net/KBz4s.png
  [5]: https://i.sstatic.net/x5IeY.png