Question in-the
In the equation above, a is a constant and 
. If the equation has two integer solutions, what is a possible value of a ?
In the equation above, a is a constant and . If the equation has two integer
Hard-difficulty · SAT Math · Nonlinear Equations in One Variable — Quadratic solving (factoring, quadratic formula, completing square). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
The correct answer is either 7, 8, or 13. Since the given equation has two integer solutions, the expression on the left-hand side of this equation can be factored as 
, where c and d are also integers. The product of c and d must equal the constant term of the original quadratic expression, which is 12. Additionally, the sum of c and d must be a negative number since it’s given that , but the sign preceding a in the given equation is negative. The possible pairs of values for c and d that satisfy both of these conditions are 
and 
, 
and 
, and 
and 
. Since the value of 
is the sum of c and d, the possible values of are 
, 
, and 
. It follows that the possible values of a are 7, 8, and 13. Note that 7, 8, and 13 are examples of ways to enter a correct answer.
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