Hyers–Ulam stability of zeros of polynomials

We prove that if | a 1 | is large and | a 0 | is small enough, then every approximate zero of the polynomial of degree n , a n z n + a n − 1 z n − 1 + ⋯ + a 1 z + a 0 = 0 , can be approximated by a true zero within a good error bound.