Let f(x)= kx^k-x^(k-1)-x^(k-2)-...-x-1, where k is an integer greater than or equal to 1. Prove the...

Let f(x)= kx^k-x^(k-1)-x^(k-2)-...-x-1, where k is an integer greater than or equal to 1. Prove the roots of f have absolute value less than or equal to 1.

This is possibly using Cauchy's Estimates for Roots of Polynomials or Ostrowski's Theorem, but I'm not sure how to use them.

Expert Solution

The problem is solved using Cauchy's bound for roots of polynomial. We need to choose the value of k to be large enough to arrive at the result.

Thank you.

Colby Messinger answered 5 months ago

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