Abstract
Let k be the number of changes of sign in the sequence of coefficients a n , an −1, … , a1, a0 in (2.8). The number of positive real roots of P(x) = 0, counting the multiplicities of the roots, is k or k minus a positive even number. If k = 1, the equation has exactly one positive real root.
Keywords
- Complex Number
- Trigonometric Function
- Hyperbolic Function
- Positive Real Root
- Approximate Root
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References
Most of these formulas can be found in any calculus text, e.g. Edwards and Penney (1998) or Sydsæter and Hammond (2005). For (2.3)–(2.12), see e.g. Turnbull (1952).
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© 2010 Springer-Verlag Berlin Heidelberg
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Sydsæter, K., Strøm, A., Berck, P. (2010). Equations. Functions of one variable. Complex numbers. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_2
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DOI: https://doi.org/10.1007/978-3-540-28518-2_2
Publisher Name: Springer, Berlin, Heidelberg
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