文献[1]~[3]对二次函数f(x)=x2+bx+c的迭代进行了探讨,其中文献[2]、[3]得到了关于方程f2(x)=x在特殊情形下根的一个结论:设f(x)=x2+bx+c,记Δ0=(b-1)2-4c,若方程f(x)=x有2个不等实根,则1)当0<Δ0<4时,f2(x)=x只有2个不等实根;2)当Δ0>4时,f2(x)=x有4个不等实根.方程f2(x)=x中的f2(x)为f2(x)=f(f(x)),一般地有fn(x)=f(fn-1(x)).本文将考虑一般二次函数f(x)=ax2+bx+c(其中a≠0且a,b,c∈R)的迭代,用初等方法给出 Literature [1]~[3] discussed the iteration of the quadratic function f(x)=x2+bx+c, where the literatures [2] and [3] got about the equation f2(x)=x in special cases. A conclusion of the next root: Let f(x)=x2+bx+c, and note that Δ0=(b-1)2-4c. If the equation f(x)=x has two unequal real roots, then 1) When 0<Δ0<4, f2(x)=x has only 2 unequal real roots; 2) When Δ0>4, f2(x)=x has 4 unequal real roots. Equation f2(x)=x The f2(x) is f2(x)=f(f(x)), and generally fn(x)=f(fn-1(x)). This article will consider the general quadratic function f(x)= The iteration of ax2+bx+c (where a ≠ 0 and a, b, c ∈ R) is given by the elementary method