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BMT 2014 Spring - Analysis P2

Source:

January 6, 2022
Polynomialsalgebrainequalities

Problem Statement

If f(x)=xn−7xn−1+17xn−2+an−3xn−3+…+a0f(x)=x^n-7x^{n-1}+17x^{n-2}+a_{n-3}x^{n-3}+\ldots+a_0 is a real-valued function of degree n>2n>2 with all real roots, prove that no root has value greater than 44 and at least one root has value less than 00 or greater than 22.
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