On the number of distinct zeros of a polynomial
In the paper the following results are proved: Theorem 1. The number of distinct zeros of a polynomial \(1+a_kz^k+ \cdots+ a_nz^n\), where \(k\leq n\) and \(a_n\neq 0\) is greater then or equal to \(k\). Theorem 2. The number of distinct zeros of the polynomial \(1+a_1z+ \cdots+ a_kz^k +a_mz^m+ \cdots +a_nz^n\), where \(0\leq k<m\leq n\), \(a_ka_ma_n\neq 0\) is greater then or equal to \(n/(n-m+k+1)\). The proofs depend on some results of the author presented in the paper ``On a problem of \textit{Young}'' in Some questions of multidimensional complex analysis, Work Collect., Krasnoyarsk 1980, 237-242 (1980; Zbl 0511.30006).
scientific article; zbMATH DE number 1131838