众所周知,求方程(1)的有理根通常运用下面的定理:“如果有理数q/p(p、q互质)是方程(1)的根,那么分子q一定是常数项a_o的因数,分母p一定是最高次项系数a_n的因数。”(该定理的证明在各种代数课本中均可查到,这里从略)。但是真正按这个定理去求整系数方程的有理根那是相当麻烦的。能否改进?可以的。我们利用下面的引理结合 It is well-known that the rational theorem of equation (1) usually uses the following theorem: “If the ration q / p (p, q) is the root of equation (1), then the numerator q must be the factor of the constant term a_o. The denominator p Must be the factor of the highest order coefficient a_n. ”(The proof of this theorem can be found in a variety of algebraic textbooks, omitted here). But according to this theorem to find the rational root of the whole coefficient equation is quite troublesome. Can you improve? Yes. We use the following lemma combination