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Prove that product of sum of roots and sum of reciprocal of roots of a polynomial with degree n is always greater than n^2 (n - square).

Questioner: Prashant

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Question:

Prove that product of sum of roots and sum of reciprocal of roots of a polynomial with degree n is always greater than n^2 (n - square).

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I don't think this is true. Do you have a proof?

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I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.**Education/Credentials**

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