MathDB

Let \begin{eqnarray*} f(x) & = & a_n x^n + a_{n-1} x^{n-1} + \cdots + a_0 \ \ \mbox{and} \\ g(x) & = & c_{n+1} x^{n+1} + c_n x^n + \cdots + c_0 \end{eqnarray*} be non-zero polynomials with real coefficients such that

g(x) = (x+r)f(x)

for some real number

r

. If

a = \max(|a_n|, \ldots, |a_0|)

and

c = \max(|c_{n+1}|, \ldots, |c_0|)

, prove that

\frac{a}{c} \leq n+1

Problem Statement