In the equation above, a is a constant and . If the equation has two integer solutions, what is a

Question

In the equation above, a is a constant and . If the equation has two integer solutions, what is a possible value of a ?

Accepted Answer

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&rsquo;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.

Question in-the