Final answer:
The relationship between Rasputin and the Romanovs contributed to their downfall by causing political instability and eroding public trust in the monarchy, which ultimately led to the Russian Revolution and the end of imperial rule.
Step-by-step explanation:
The relationship between Rasputin and Tsar Nicholas II and Tsarina Alexandra significantly contributed to the downfall of the Romanov dynasty, marking the end of imperial Russia. The Romanovs were steeped in controversy due to Alexandra's heavy reliance on Rasputin, who was seen as a mystical healer for the heir to the throne, Alexei, who suffered from hemophilia. This relationship caused unease among the nobility and general populace, who viewed Rasputin's influence with suspicion and contempt. The tsarina's faith in Rasputin led to further estrangement from the Russian people.
During World War I, as the tsar took command at the front, leaving Alexandra and Rasputin to effectively govern, the country saw increased political instability and autocratic rule, which exacerbated the public's disenchantment with the monarchy. The aristocracy was divided, corruption was rampant, and the empire's ability to govern effectively was severely undermined. Rasputin's murder by Russian nobles in 1916 reflected the desperation to remove his influence, but it was too late; the damage to the Romanov reputation had been done, and the stage was set for the Russian Revolution of 1917 that led to the fall of the Romanovs and the rise of socialism in Russia.