To solve this SE question, let us deploy IMS's four-step technque.

STEP #1 -> STORYBOARD

Let us first read and understand the story.



The story tells us that America's founding fathers used compromise to do something to disagreements. As per the story, these disagreements arose while assaying (assessing) the emerging government. The author gives an example of how compromise was used: The founders decided that creating a two-house legislative body would be the best solution to suppress conflicts between two factions over how citizens would be represented in the national government.

STEP #2-> RELATE

To find a contextual fit for the blank, let us ask ourselves two questions.

-> What does the blank deal with?
-> What information do we have about what the blank deals with?

So, what does the blank deal with?
The blank deals with an action performed by compromise on disagreements.

And what information do we have about compromise?
It was used to suppress conflicts between two factions over how citizens would be represented in the national government.

STEP #3 -> PREDICT

Let us now come up with our own word for the blank. Since we know compromise was used to suppress conflicts (disagreements), 'SUPPRESS' can be our own word for the blank.

STEP #4 -> ELIMINATE

Options that do not closely match with 'SUPPRESS' can be eliminated.

A. quell | AN EXCELLENT MATCH | Means 'suppress' or 'subdue' | KEEP
B. castigate | NOT A MATCH | Means 'reprimand severaly' or 'punish in order to correct' | ELIMINATE
C. emulate | NOT A MATCH | Means 'try to equal or surpass, especially by copying' | ELIMINATE
D. exacerbate | NOT A MATCH | Means 'intensify' or 'aggravate' | ELIMINATE
E. obviate | A CLOSE MATCH | Means 'avoid or prevent (difficulties, disadvantages, etc.) by effective measures' | KEEP
F. precipitate | NOT A MATCH | Means 'cause to happen sooner than expected' | ELIMINATE

Hence, (A) and (E) are the correct answers.