Despite initial public skepticism, the scientist's _____ approach to the long-standing problem ultimately yielded groundbreaking results, proving that unconventional methods can sometimes be the most effective.

✓ Correct Answer: Option B

The sentence indicates the approach was 'unconventional' and challenged 'long-standing' methods, leading to 'groundbreaking results.' 'Heretical' (departing from accepted beliefs or standards) best fits this context of an unconventional, successful challenge to orthodoxy.