Where are you? Are you planting them inside?
Turmeric purchased at the store may be very slow to germinate, as it is often treated to prevent germination. It can throw that off, if the root doesn't rot or dry up. The first time I grew turmeric it took nearly a year to sprout.
If you can get it from the ethnic stores it's less likely to be treated.
Find roots with growth buds. The first image is best. (These are ginger pictures, but the idea is the same).
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