Hyers–Ulam stability of zeros of polynomials

We prove that if |a1||a1| is large and |a0||a0| is small enough, then every approximate zero of the polynomial of degree nn, anzn+an−1zn−1+⋯+a1z+a0=0anzn+an−1zn−1+⋯+a1z+a0=0, can be approximated by a true zero within a good error bound.