We consider the problem of producing all the roots of a polynomialp(x) =a0xn+a1xn−l+ … +an(where all the roots are distinct) by an iterative systolic array. Two basic arrays are considered, one where the position of the roots remain stationary and another where they are non-stationary. The former scheme requiresO(n) basic cells, the latterO(z) cells withz(>0) a suitably chosen constant determining the number of root approximations on a single pass through the array. Finally an area efficient systolic ring is discussed requiringO(n/A) cells to compute an arbitrary number of root approximations.