Estimate of a sum of Legendre symbols of polynomials of even degree

Let n≥4 be even, p > (n²?2n)/2 be simple odd, andf(x)=a ₀+a ₁+...+a _nxⁿ be a polynomial with integral coefficients that are not quadratic over the residue field modulo p, (a _n, p)=1. The following inequality is proved: $$left| {sumnolimits_{x = 1}^p {left( {frac{{f(x)}}{p}} right)} } right| leqslant (n - 2)sqrt {p + 1 - frac{{n(n - 4)}}{4}} + 1.$$