In addition to the great benefits mankind has enjoyed since the discovery of certain technologies, many atrocities would have been prevented had the scientists who made the discoveries had the wisdom to discard such power.

A. had the scientists who made the discoveries had
B. if the scientists who made the discoveries have had
C. if the scientists who made the discoveries had
D. had the scientists who made the discoveries have
E. had the scientists who made the discoveries showed

Answer choice A is the only grammatically correct one. The conditional in this question begins with the result part (many atrocities would have been prevented) and continues with the condition part (had the scientists... power).
The result part is not underlined, so it must be correct. It is in Future Past Perfect (would have been), which indicates Conditional 3. Therefore, the condition part must also be consistent with Conditional 3, that is, must be in Past Perfect, as is the case in this answer choice (had had).
In Conditional 3 sentences, "if" may be omitted, in which case the condition part begins with the word had (as it does in this and in some of the other answer choices). Answer choice B is grammatically incorrect because the condition part is in Present Perfect (if... have had). Answer C is also grammatically incorrect. The condition part is in Past Simple (if... had), which indicates Conditional 2, while the result part is in Future Past Perfect (would have been), indicating Conditional 3.
What is confusing about this answer choice is the use of the verb had in the condition part. Since had is also used in Conditional 3 sentences (only there it is followed by a verb in the third form - V3), it is easy to mistake the condition part for that of a Conditional 3.
Answer D is grammatically incorrect. The condition part should be consistent with Conditional 3, that is, must be in Past Perfect. The Past Perfect structure is had + V3. However, in this answer choice the verb had is followed by a verb in Base form (have).
Finally answer choice E is also grammatically flawed. In this answer choice the verb had is followed by a verb in past form (showed) in the condition clause. The third form of the verb show is shown.
Another way of identifying the grammatical incorrectness of this answer choice is the following: The verb showed is conjugated - it is in the past form (V2). The first verb, and only the first verb, of a sentence must be conjugated. Since showed is not the first verb (had is), it shouldn't be conjugated.