(ax + b)(bx + a) = 60x^2 + v * x + 60
(ab)x^2 + ( a^2 + b^2)x + (ab) = 60x^2 + vx + 60
It's obvious that ab = 60
And (a^2 + b^2) = v
Divisors of 60 =
1 | 2 | 3 | 4 | 5 | 6 | 10 | 12 | 15 | 20 | 30 | 60
The minimum value for a^2 + b^2 = v will be produced when a = 6 and b =10
So
v = (6)^2 + (10)^2 = 136