India TST : Day3 :Problem 3
Source: easy
May 22, 2009
algebrapolynomialalgebra proposed
Problem Statement
Let
f(x)\equal{}\sum_{k\equal{}1}^n a_k x^k and g(x)\equal{}\sum_{k\equal{}1}^n \frac{a_k x^k}{2^k \minus{}1} be two polynomials with real coefficients.
Let g(x) have 0,2^{n\plus{}1} as two of its roots. Prove That has a positive root less than .