Title: Cubic polynomials with real or complex coefficients: The full picture
Abstract: The cubic polynomial with real coefficients y = ax3 + bx2 + cx + d in which a ≠ 0, has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance mathematics in Italy various techniques have been developed which yield the three roots of a general cubic equation. A 'cubic formula' does exist - much like the one for finding the two roots of a quadratic equation - but in the case of the cubic equation the formula is not easily memorised and the solution steps can get quite involved (Abramowitz and Stegun, 1970; see Chapter 3: Elementary Analytical Methods, 3.8.2 Solution of Cubic Equations). Hence it is not surprising that with the advent of the digital computer, numerical rootfinding algorithms such as those attributed to Newton-Raphson, Halley, and Householder have become the solution of choice (Weisstein, n.d.).
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: article
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Cited By Count: 4
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