The quadratic equation x^2 - ax + 2016 + 5 = 0 has two postiive integer solutions. Find the minimum value of a.

Guest Jan 7, 2021

#2**0 **

We might also take the discriminant, b^2 - 4ac.

We have that (-a)^2 - 4 * 2016 * 1 > 1, so a^2 - 8064 > 0. Thus, a^2 > 8064, and a > ±√8064, so a> about 89.8 and a< about -89.8. However, we would like to find the integer solutions, which means a must be an integer, which means that a ≤ -90.

(By the way CPhill, you have a typo on the first line)

Pangolin14 Jan 8, 2021