Abstract / Excerpt:

Objective: This investigation explored and expounded more the nature of both cubic and quartic equations, with emphasis on the easy approach to their algebraic and basic applications to other areas of mathematics, engineering, and physical sciences.
Methodology: The investigator used the content analysis method.
Conclusion: (1) The cubic equation x3 + ax2 + bx + c = 0, with b = a2, a, being an element of Z+, and c = -a3(n3 + n2 + n), n, being a positive integer, has a simplified algebraic solution through the n3 + n2 + n table. The essential step in the method requires substitution of x by an resulting to an equation having the same value of coefficients in the terms containing n. Transposition, application of division property of equality, and lastly verification with the table eventually complete the easy method. (2) In general physics, especially in bouyancy, the determination of the depth of the sphere's immersion in a fluid leads to cubic equation because this involves the volume of the spherical segment of one base. This is a consequence of the application of Archimedes' principle, specifically that case of a partially submerged solid in a liquid. The cubic equation results from the involvement of the formula for the volume of the spherical segment of one base, V = (1/6)æh(3r2 + h2).

Info

Source Institution	Ateneo de Davao University
Unit	Natural Science
Authors	Limjuco, Renan Preyas,
Page Count	1
Place of Publication	Davao City
Original Publication Date	March 4, 1996
Tags	Dissertations, Mathematics

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