MediumMath· Advanced Math· Nonlinear equations in one variable and systems of equations in two variables· SPR
In the equation above, a is a constant and . If the equation has two integer solutions, what is a possible value of a ?
Correct answer: 7 or 8 or 13
(parsed from the explanation — this source omits an answer key
for this item)
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.
SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.
id cb_question_bank:5240ad4b-bdec-420e-b14c-2fbe39cbe33e · question a4f61d75 · IBN 070620-DC
· JSON