Quadratic formula (original) (raw)
الصيغة التربيعية (بالإنجليزية: Quadratic formula) هي عبارة رياضية لحل المعادلات التربيعية. توجد طرق أخرى لحل المعادلات التربيعية مثل التحليل إلى عوامل وإكمال المربع أو الرسم البياني ولكن غالباً ما يكون استخدام الصيغة التربيعية أكثر ملائمة من الطرق الأخرى. الشكل العام للمعادلة التربيعية هو: هنا x يمثل المجهول، بينما a، b، و c هي حدود ثابتة بحيث a لايساوي الصفر. الصيغية التربيعية هي: وما تحت الجذر يسمى المميز.
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dbo:abstract | الصيغة التربيعية (بالإنجليزية: Quadratic formula) هي عبارة رياضية لحل المعادلات التربيعية. توجد طرق أخرى لحل المعادلات التربيعية مثل التحليل إلى عوامل وإكمال المربع أو الرسم البياني ولكن غالباً ما يكون استخدام الصيغة التربيعية أكثر ملائمة من الطرق الأخرى. الشكل العام للمعادلة التربيعية هو: هنا x يمثل المجهول، بينما a، b، و c هي حدود ثابتة بحيث a لايساوي الصفر. الصيغية التربيعية هي: وما تحت الجذر يسمى المميز. (ar) Στην στοιχειώδη άλγεβρα, ο τετραγωνικός τύπος είναι η λύση της δευτεροβάθμιας εξίσωσης. Υπάρχουν και άλλοι τρόποι για να λυθεί η εξίσωση αντί να χρησιμοποιηθεί ο τετραγωνικός τύπος, όπως είναι η παραγοντοποίηση, η συμπλήρωση τετραγώνου, ή να δώθει με γραφική παράσταση. Η χρήση του τετραγωνικού τύπου είναι συνήθως ο πιο εύχρηστος τρόπος. Η γενική εξίσωση είναι: Εδώ το x αντιπροσωπεύει έναν άγνωστο, ενώ τα a, b, και c είναι σταθερές με το α να είναι διάφορο του μηδενός. Μπορεί κάποιος να επαληθεύσει ότι ο τετραγωνικός τύπος ικανοποιεί την δευτεροβάθμια εξίσωση, εισάγοντας του πρώτου στη δεύτερη. Κάθε μία από τις λύσεις που δίνεται από το τετραγωνικό τύπο ονομάζεται ρίζα της εξίσωσης. Γεωμετρικά, αυτές οι ρίζες αντιπροσωπεύουν τις τιμές του x για τις οποίες οποιαδήποτε παραβολή, που δίνεται ρητά ως y = ax2 + bx + c, διασχίζει τον x-άξονα. Καθώς επίσης είναι ένας τύπος που θα παράγει τα μηδενικά οποιασδήποτε παραβολής, η δευτεροβάθμια εξίσωση θα δώσει τον άξονας συμμετρίας της παραβολής, και μπορεί να χρησιμοποιηθεί για να προσδιορίσει αμέσως πόσα μηδενικά να περιμένουμε να έχει η παραβολή. (el) In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. Given a general quadratic equation of the form with x representing an unknown, with a, b and c representing constants, and with a ≠ 0, the quadratic formula is: where the plus–minus symbol "±" indicates that the quadratic equation has two solutions. Written separately, they become: Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax2 + bx + c, crosses the x-axis. As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains. The expression b2 − 4ac is known as discriminant. If b2 − 4ac ≥ 0 then the square root of the discriminant will be a real number; otherwise it will be a complex number. If a ≠ 0, b, and c are real numbers then 1. * If b2 − 4ac > 0 then we have two distinct real roots/solutions to the equation ax2 + bx + c = 0. 2. * If b2 − 4ac = 0 then we have one repeated real solution. 3. * If b2 − 4ac < 0 then we have two distinct complex solutions, which are complex conjugates of each other. (en) Dalam aljabar elementer, rumus kuadrat adalah rumus yang memberikan solusi untuk sebuah persamaan kuadrat. Ada cara lain untuk menyelesaikan persamaan kuadrat selain menggunakan rumus kuadrat, seperti faktorisasi (pemfaktoran langsung, pengelompokan, metode AC), , ,dan lain sebagainya. Diberikan persamaan kuadrat umum dalam bentuk dengan mewakili suatu variabel yang tidak diketahui. Variabel , , dan mewakili konstanta dengan , rumus kuadratnya adalah: dimana tanda plus-minus "±" menunjukkan bahwa persamaan kuadrat memiliki dua solusi. Dengan menulisnya secara terpisah, maka diperoleh: dan . Masing-masing dari dua solusi ini juga disebut akar dari persamaan kuadrat. Secara geometris, akar-akar tersebut mewakili nilai di mana suatu parabola , memotong sumbu . Selain menjadi rumus yang memberikan nilai nol dari suatu parabola, rumus kuadrat juga dapat digunakan untuk mengidentifikasi sumbu simetri parabola, dan jumlah bilangan real nol yang terdapat di persamaan kuadrat. (in) En algèbre classique, la formule quadratique est la solution de l'équation du second degré. Il y a d'autres façons pour résoudre l'équation du second degré au lieu d'utiliser la formule quadratique, comme la factorisation, la méthode de complétion du carré ou le tracé du graphe. Mais utiliser la formule quadratique est souvent la façon la plus pratique. L'équation du second degré générale est : Ici, x représente une valeur inconnue alors que a, b et c sont constantes, avec a non nul. En insérant la formule quadratique dans l'équation du second degré, on peut vérifier que la formule quadratique satisfait l'équation du second degré. Les deux solutions données par la formule quadratique sont les racines de l'équation. (fr) 二次方程式の解の公式(にじほうていしきのかいのこうしき)とは、未知数が一つの二次方程式の解を、式の係数を代入することにより求めることができる公式である。 (ja) Met behulp van de wortelformule of abc-formule kunnen de oplossingen van een kwadratische of vierkantsvergelijking worden gevonden. De oplossingen worden ook de wortels van de vergelijking genoemd. Het zijn de nulpunten van de betrokken tweedegraadsveelterm. (nl) Em álgebra, a fórmula quadrática, também conhecida como fórmula de Bhaskara no Brasil, é uma fórmula que fornece a solução de uma equação do 2º grau (ou equação quadrática). Existem outras formas de resolver uma equação quadrática, como fatoração, completamento de quadrados, pelo gráfico da função e outras. Dada uma equação quadrática geral no formato: cujo discriminante é positivo (onde representa um valor desconhecido, , e representam constantes, sendo ), a fórmula quadrática é: na qual o sinal de mais ou menos "±" indica que a equação quadrática tem duas soluções. Quando escritas separadamente, estas são: Cada uma dessas duas soluções é chamada de raiz (ou zero) da equação quadrática. Geometricamente, essas raízes representam os valores de em que qualquer parábola, descrita como , cruza o eixo . Além de ser uma fórmula que fornece as raízes de qualquer parábola, a fórmula quadrática também pode ser usada para identificar o eixo de simetria da mesma parábola, e o número de raízes reais que uma equação quadrática contém. Embora no Brasil seja comumente atribuída a Bhaskara II, uma variante da fórmula que fornece a raiz real de uma equação quadrática já havia sido descoberta séculos antes do nascimento de Bhaskara, pelo matemático indiano Brahmagupta. Em partes da Alemanha e da Suíça, a fórmula é coloquialmente conhecida como a "fórmula da meia-noite", porque os alunos devem ser capazes de recitá-la mesmo que sejam acordados à meia-noite. (pt) |
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rdfs:comment | الصيغة التربيعية (بالإنجليزية: Quadratic formula) هي عبارة رياضية لحل المعادلات التربيعية. توجد طرق أخرى لحل المعادلات التربيعية مثل التحليل إلى عوامل وإكمال المربع أو الرسم البياني ولكن غالباً ما يكون استخدام الصيغة التربيعية أكثر ملائمة من الطرق الأخرى. الشكل العام للمعادلة التربيعية هو: هنا x يمثل المجهول، بينما a، b، و c هي حدود ثابتة بحيث a لايساوي الصفر. الصيغية التربيعية هي: وما تحت الجذر يسمى المميز. (ar) 二次方程式の解の公式(にじほうていしきのかいのこうしき)とは、未知数が一つの二次方程式の解を、式の係数を代入することにより求めることができる公式である。 (ja) Met behulp van de wortelformule of abc-formule kunnen de oplossingen van een kwadratische of vierkantsvergelijking worden gevonden. De oplossingen worden ook de wortels van de vergelijking genoemd. Het zijn de nulpunten van de betrokken tweedegraadsveelterm. (nl) Στην στοιχειώδη άλγεβρα, ο τετραγωνικός τύπος είναι η λύση της δευτεροβάθμιας εξίσωσης. Υπάρχουν και άλλοι τρόποι για να λυθεί η εξίσωση αντί να χρησιμοποιηθεί ο τετραγωνικός τύπος, όπως είναι η παραγοντοποίηση, η συμπλήρωση τετραγώνου, ή να δώθει με γραφική παράσταση. Η χρήση του τετραγωνικού τύπου είναι συνήθως ο πιο εύχρηστος τρόπος. Η γενική εξίσωση είναι: (el) En algèbre classique, la formule quadratique est la solution de l'équation du second degré. Il y a d'autres façons pour résoudre l'équation du second degré au lieu d'utiliser la formule quadratique, comme la factorisation, la méthode de complétion du carré ou le tracé du graphe. Mais utiliser la formule quadratique est souvent la façon la plus pratique. L'équation du second degré générale est : (fr) In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. Given a general quadratic equation of the form with x representing an unknown, with a, b and c representing constants, and with a ≠ 0, the quadratic formula is: where the plus–minus symbol "±" indicates that the quadratic equation has two solutions. Written separately, they become: (en) Dalam aljabar elementer, rumus kuadrat adalah rumus yang memberikan solusi untuk sebuah persamaan kuadrat. Ada cara lain untuk menyelesaikan persamaan kuadrat selain menggunakan rumus kuadrat, seperti faktorisasi (pemfaktoran langsung, pengelompokan, metode AC), , ,dan lain sebagainya. Diberikan persamaan kuadrat umum dalam bentuk dengan mewakili suatu variabel yang tidak diketahui. Variabel , , dan mewakili konstanta dengan , rumus kuadratnya adalah: dimana tanda plus-minus "±" menunjukkan bahwa persamaan kuadrat memiliki dua solusi. Dengan menulisnya secara terpisah, maka diperoleh: dan . (in) Em álgebra, a fórmula quadrática, também conhecida como fórmula de Bhaskara no Brasil, é uma fórmula que fornece a solução de uma equação do 2º grau (ou equação quadrática). Existem outras formas de resolver uma equação quadrática, como fatoração, completamento de quadrados, pelo gráfico da função e outras. Dada uma equação quadrática geral no formato: cujo discriminante é positivo (onde representa um valor desconhecido, , e representam constantes, sendo ), a fórmula quadrática é: (pt) |
rdfs:label | صيغة تربيعية (ar) ABC-Formel (de) Τετραγωνικός τύπος (el) Rumus kuadrat (in) Formule quadratique (fr) 二次方程式の解の公式 (ja) Wortelformule (nl) Quadratic formula (en) Fórmula quadrática (pt) |
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