A rod of length 1 meter has variable coefficient of thermal expansion $\alpha =(1.67+1.67x-1.67x^2)\times {10}^{-4}$    (in SI unit). The rod is uniform throughout and its  Young’s modulus is same throughout the rod. Rod is rigidly fixed between two vertical  walls. Find the distance x (in SI unit) of the point of the rod from corner x = 0 which is  not displaced from its position on heating the rod by  $1^{\circ }C$. (Given that x is neither 0 nor 1)