The correct option is
D have liked
Answer : D
Explanation :
The first sentence is in the present tense.
And the second sentence suggests us about a past experience (all my life) having a connection with the present (love rock and roll).
To grammatically expresses such situations where there is a connection of past with the present, the Present Perfect Tense is used.
Basically,
Present Perfect Tense = A helping verb (have/has) + Past Participle form of the verb.
The sentence is first person singular ("I" in the sentence), thus we will use the helping verb "have".
The past participle form of the verb, like is liked.
Thus to complete the sentence to Present Perfect Tense we have to fill the blank with = have + liked.
That is, option D.
Therefore the correct complete sentence is :
I love rock and roll. I HAVE LIKED it all my life.