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Proof of Newton's inequalities
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Classroom Contents
Real-Rooted Polynomials
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- 1 Intro
- 2 The Fundamental Theorem of Algebra
- 3 Roots vs. coefficients
- 4 Newton's identities
- 5 Checking real-rootedness
- 6 Interlacing of roots
- 7 Derivative of a real-rooted polynomial
- 8 Reversion of the order of coefficients
- 9 Proof of Newton's inequalities
- 10 Connection with independent Bernoulli variables
- 11 Combinatorial examples of real-rooted polynomials
- 12 Curious fact about random spanning trees
