关于一元多项式的Casas-Alvero猜想一类情况研究

Study on the Casas-Alvero Conjecture of Univariate Polynomials

令f(x)是首项系数等于1的复系数一元多项式,本文利用高等代数知识去证明了:如果f(x)恰有2个不同的根,则f(x)不是Casas-Alvero多项式,上述结果部分地解决了Casas-Alvero猜想。

Let f(x)be a monic complex univariate polynomial with the leading coefficient is equal to 1.This paper uses the knownledge of higher algebra to prove that if f(x)has exactly two distinct roots,then f(x)is not a Casas-Alvero polynomial.The above mentioned result partly verifies the Casas-Alvero conjecture.