It is given that a function $f{x} = x^3 - 6x^2 + ax+ b $ on [1,3] , Rolle's theorem holds with $c = 2 + \frac{1}{\sqrt3}$. Find the value of a and b if f(1) = f(3) = 0

Question

$(A)\;a = 11 , b = -6$
$(B)\;a = 10 , b = -5$
$(C)\;a = -11 , b = 6$
$(D)\;a = -10 , b = 5$