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Hudde’s Two Rules for Polynomials: Maximizing Understanding

Explore Johannes Hudde’s rules for polynomials applied in various fields. Learn how to identify local extremes and double roots in equations. Gain insights into coefficient reduction and practical applications in finance and army strategy.

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Hudde’s Two Rules for Polynomials: Maximizing Understanding

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  1. Hudde’s Two Rulesfor Polynomials Pre-May Seminar March 14, 2011

  2. Johannes Hudde (1628-1704)

  3. Johannes Hudde (1628-1704) • Amsterdam Burgomaster: 1672-1703

  4. Johannes Hudde (1628-1704) • Amsterdam Burgomaster: 1672-1703 • Epistolasecunda, de maximis et minimis 1658

  5. Johannes Hudde (1628-1704) • Amsterdam Burgomaster: 1672-1703 • Epistolasecunda, de maximis et minimis 1658 • De reductioneaequationum: Coefficients

  6. Johannes Hudde (1628-1704) • Amsterdam Burgomaster: 1672-1703 • Epistolasecunda, de maximis et minimis 1658 • De reductioneaequationum: Coefficients • Slows French Army

  7. Johannes Hudde (1628-1704) • Amsterdam Burgomaster: 1672-1703 • Epistolasecunda, de maximis et minimis 1658 • De reductioneaequationum: Coefficients • Slows French Army • Pricing Annuities

  8. Hudde’s Two Rules • Rule 1: If the polynomial an xn + an-1 xn-1 +…+ a1 x + a0 has a local max or local min @ x=x0, then x=x0 is a root of the equation nanxn + (n-1)an-1 xn-1 +…+ 2a2x2 + a1 x=0.

  9. Hudde’s Two Rules • Rule 2: If the polynomial equation an xn + an-1 xn-1 +…+ a1 x + a0 =0 has a double root @ x=x0, and if b0 , b1 ,…, bn are numbers in arithmetic progression, then x=x0 is a root of the poly equation an b0 x n + an-1 b1 xn-1 +…+ a1bn-1 x + a0 bn=0.

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