Question

Suppose a, b are integers and a + b is a root of x² + ax + b = 0. What is the maximum possible value of b²?

Answer 1

As a, b ∈ I, a² + 6a + 1 must be a perfect square a(a + 6) + 1 must be a perfect square

Possible values of a are a = 0 or a = –6

If a = 0, b = –1 or 0

If a = –6, b = 9 or 8

Maximum possible value of b² = 81