一类根式不可解代数方程

A Type of Unsolvable Algebra Equations by Radicals

利用克罗内克定理给出了构造不可解代数方程的如下的一个充分条件 :设整系数 n次多项式 f ( x)在有理数域 Q上不可约 ,如果代数方程 f ( x) =0的实根个数 t满足 :1<t<n,则此代数方程不可根式求解 .并且利用上述充分条件构造出一类根式不可解的代数方程——实系数

This paper provided the following suffi ci ent condition for constructing the unsolvable algebra equations by radicals:Let the integral coefficient polynomial f(x)is irreducible in the rational numbe r field Q,if t,the number of real roots of algebra equa tion f(x)=0 satisfies 1<t<n,then the equation is unsolvable.Based on the obove coudition,a type of unsolvable algebra equations of real coefficient trin omial is constructed.