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Hudde’s Two Rules for Polynomials

Hudde’s Two Rules for Polynomials. Pre-May Seminar March 14, 2011. Johannes Hudde (1628-1704). Johannes Hudde (1628-1704). Amsterdam Burgomaster: 1672-1703. Johannes Hudde (1628-1704). Amsterdam Burgomaster: 1672-1703 Epistola secunda , de maximis et minimis 1658.

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Hudde’s Two Rules for Polynomials

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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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