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master's thesis
Polinomi u jednoj varijabli
2022. urn:nbn:hr:126:120787
Cvenić, Doris
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Cite this document

Cvenić, D. (2022). Polinomi u jednoj varijabli (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:120787

Cvenić, Doris. "Polinomi u jednoj varijabli." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:120787

Cvenić, Doris. "Polinomi u jednoj varijabli." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:120787

Cvenić, D. (2022). 'Polinomi u jednoj varijabli', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 19 October 2024, https://urn.nsk.hr/urn:nbn:hr:126:120787

Cvenić D. Polinomi u jednoj varijabli [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 October 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:120787

D. Cvenić, "Polinomi u jednoj varijabli", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:120787

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Metadata
TitlePolinomi u jednoj varijabli
Title (english)Polynomials in One Variable
AuthorDoris Cvenić
MentorLjiljana Primorac Gajčić (mentor)
Committee memberMihaela Ribičić Penava (predsjednik povjerenstva)
Committee memberLjerka Jukić Matić (član povjerenstva)
Committee memberLjiljana Primorac Gajčić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-10-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom radu proučavani su polinomi u jednoj varijabli. Nakon njihova definiranja, prikazane su računske operacije s polinomima te je dokazano da skup svih polinoma čini prsten. Zatim je, pomoću Teorema o nul-polinomu, dokazan i Teorem o jednakosti polinoma. Opisano je kada su polinomi djeljivi i Hornerov algoritam za dijeljenje polinoma linearnim polinomom. Definirana je najveća zajednička mjera dvaju polinoma te je Euklidovim algoritmom prikazan postupak traženja iste. Proučavane su i nultočke polinoma, njihova svojstva i faktorizacija polinoma nakon koje je dokazan Vieteov teorem. Potom su definirane algebarske jednadžbe i objašnjeni su postupci traženja cjelobrojnih, racionalnih i kompleksnih rješenja. Za kraj, definirana je reducibilnost i ireducibilnost polinoma te derivacija polinoma i njihova svojstva.
Abstract (english)
In this work, polynomials in one variable were studied. After defining them, computational operations with polynomials were presented and it was proved that the set of all polynomials forms a ring. Then, using the Zero polynomial theorem, the Theorem of polynomial equality was also proved. It is described when polynomials are divisible and Horner’s algorithm for dividing a polynomial by a linear polynomial is given. The largest common measure of two polynomials is defined, and the procedure for finding it using the Euclidean algorithm is presented. Zeros of polynomials, their properties and factorization of polynomials were also studied, afterwards Vi`ete’s theorem was proved. Algebraic equations are then defined and the procedures of searching for integer, rational and complex solutions are explained. Finally, the reducibility and irreducibility of polynomials and the derivation of polynomials and their properties are defined.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:120787
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-10-14 09:18:28