I wash my hair, but at the roots it's always still greasy?

Don't condition the roots, just the ends.

Years (decades?) ago, a stylist told me that I should apply shampoo only above the ears and only apply conditioner below the top of the ears. As you wash/condition it distributes itself through your hair but with much better balance. It made a real difference in the overall condition of my hair.

Thank you so much, lifesaver! x

Yes agreed with Jespeh you should not condition the roots, just the ends.