Document Zbl 07602738

Elementary theory of cubics and quartics. (English) Zbl 07602738

Liet. Mat. Rink., Proc. Lith. Math. Soc., Ser. A 58, 16-22 (2017).

MSC:

12D10	Polynomials in real and complex fields: location of zeros (algebraic theorems)
26C10	Real polynomials: location of zeros

Keywords:

cubic equation; quartic equation; rational solutions; factorization

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References:

[1]	by 4p, we get the cubic equation (cf. [1, 3])
[2]	A.G. Kurosh. Kurs vysshey algebry. Moskva, Nauka, 2011.
[3]	E.W. Weisstein. “Cubic formula”. From MathWorld -A Wolfram Web Resource. Avail-able from Internet: http://mathworld.wolfram.com/CubicFormula.html.
[4]	E.W. Weisstein. “Quartic equation”. From MathWorld -A Wolfram Web Resource. Avail-able from Internet: http://mathworld.wolfram.com/QuarticEquation.html.
[5]	Įrodyta, kad trečiojo ir ketvirtojo laipsnio lygtis realiųjų skaičių aibėje galima išspręsti elementariai -nesiremiant nei kompleksiniais skaičiais, nei išvestinėmis. Pateikti atitinkami algoritmai.
[6]	Raktiniai žodžiai: trečiojo laipsnio lygtys, ketvirtojo laipsnio lygtys, racionalieji sprendiniai, daugia-narių skaidymas.

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