Function f (x) is defined as R, satisfying f (x) = f (14-x), equation f (x) = 0 has n real roots, the sum of these n roots is 2009, then n is to process, fast

Function f (x) is defined as R, satisfying f (x) = f (14-x), equation f (x) = 0 has n real roots, the sum of these n roots is 2009, then n is to process, fast

Because f (x) = f (14-x), the axis of symmetry of the function is (x + 14-x) / 2 = 7, that is, x = 7, that is, the sum of every two is 14. X = 7 may or may not be a root. If it is not a root, 2009 / 14 should be an integer, but 2009 / 14 = 143.5, which is not the problem. So x = 7 is a root. Subtract this heel, and the rest is the sum of every two is 14