محمد راضى سعد حسن

المزيد من المعرفة

العلاقة بين جذري معادلة الدرجة الثانية ومعاملات حدودها

جذري المعادلة التربيعية

بحل المعادلة التربيعية التالية: ax²+bx+c=0 ينتج حلان يسمى جذري المعادلة التربيعية، وقيمتهم موضحة في الصورة التالية.

مجموع الجذرين

إذا قمنا بجمع جذري المعادلة التربيعية تكون قيمة الجمع (-معامل x مقسومًا على معامل ax²) أي أن مجموع الجذرين = -b÷a.

حاصل ضرب الجذرين

إذا قمنا بضرب جذري المعادلة التربيعية تكون قيمة الضرب (الحد المطلق مقسومًا على معامل ax²) أي أن حاصل ضرب الجذرين = c÷a.

ملحوظات هامة

إذا كان أحد الجذرين مركب غير حقيقي، يكون الجذر الاخر هو مرافق للجذر.
إذا كان جذر المعادلة معكوس جمعي للاخر، يكون مجموع الجذرين يساوي صفر.
إذا كان جذر المعادلة معكوس ضربي للاخر، يكون حاصل ضرب الجذرين يساوي واحد.

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