In this paper we investigate quaternion polynomial equations with imprecisely defined coefficients, an area not previously explored. To address this uncertainty, we introduce the concept of a closed quaternion ball and develop arithmetic operations for these sets. Within this framework, we analyze specific classes of equations and identify the conditions under which solutions exist. The approach allows us to represent the solution sets within closed quaternion balls, thereby capturing the range of all possible values. In particular, we examine quadratic and cubic equations in detail and derive a quaternionic analogue of the de Moivre formula, providing explicitly the n-th roots of a closed quaternion ball.