Source : Webster's Revised Unabridged Dictionary (1913)

Ineradicable \In`e*rad"i*ca*ble\, a.
   Incapable of being ?radicated or rooted out.

         The bad seed thus sown was ineradicable. --Ld. Lytton.

Source : WordNet®

ineradicable
     adj : not able to be destroyed or rooted out; "ineradicable
           superstitions" [ant: {eradicable}]