Priority areas for applying artificial intelligence to pedagogical education

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25.04.2026
75
Oʻzbekcha

KUB TENGLAMA VA UNING TURLI HAQIQIY ILDIZLARI HAQIDA MASALA

Published
25.04.2026
Journal
Priority areas for applying artificial intelligence to pedagogical education
Issue
Priority areas for applying artificial intelligence to pedagogical education
Pages
517-520
DOI
10.5281/zenodo.20215037

Authors

Abdiyeva Shoira Shukurovna

Abstract

Ushbu maqolada kub tenglama uchta haqiqiy ildizlarga ega bo‘lib, ulardan biri yoki uchtasi ham musbat bo‘lgan holat uchun teoremalar keltirib chiqarilgan. Bunda kub tenglama koeffisiyentlari va kub funksiya ekstremumlari qiymatlari ko‘paytmasining ahamiyati ochib berilgan. Teoremalar kvadrat va kub funksiya grafiklarini tahlil qilish orqali keltirib chiqarilgan. Teoremalarda keltirilgan shartlarni sun’iy intellekt (ChatGPT) ga generatsiya qilish orqali kub tenglama ildizlar soni bilan birga ildizlari ishorasini bashorat qilish imkonini beradi.

Keywords

sun’iy intellekt Kvadrat tenglama kub tenglama kub funksiya ekstremum qiymatlar

Other language versions

Русский
В данной статье рассматриваются теоремы для случая, когда кубическое уравнение имеет три действительных корня, из которых один или все три являются положительными. При этом раскрывается значение произведения коэффициентов кубического уравнения и значений экстремумов кубической функции. Теоремы получены на основе анализа графиков квадратной и кубической функций.
Квадратное уравнение кубическое уравнение кубическая функция значения экстремумов
English
This article presents theorems for the case when a cubic equation has three real roots, one or all three of which are positive. The significance of the product of the coefficients of the cubic equation and the extrema values of the cubic function is revealed. The theorems are derived through the analysis of the graphs of quadratic and cubic functions.
Quadratic equation cubic equation cubic function extrema values

References

1. Abdiyeva Sh.Sh. O‘quvchilarning vizual tafakkurini rivojlantirishda loyihalash metodidan foydalanish.// “Ilm sarchashmalari” jurnali.-2023., - №3. 65-70 b.
2. Abdiyeva Sh.Sh., Turgunbayev R.M. Theorems on the number of roots of a cubic equation and their location as a means of developing students' visual thinking. //Fiziko-matematichna osvita. - 2023. – No.4. - P.7-13. https://doi.org/10.31110/2413-1571-2023-038-4-001
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