IKMC 2027 - Grades 9-10 - Self-study SET 2 - Thematic Batch 3 Question 28

Let n be a positive integer such that the two equations $x^2+ax+2=0$ and $x^2+2x+a=0$ have all their roots integers. The sum of the squares of the roots of the first equation equals that of the second. What is a?