5.2-bo'lim : ko'phadlarning nollari/ildizlari
1. Quyidagi ko‘phadning barcha nollarini sanab bering va ularning ko‘paytmalarini keltiring.
\[f\left( x \right) = 2{x^2} + 13x - 7\]Yechim
Ushbu muammoni hal qilish uchun biz birinchi navbatda ko'phadni hisobga olishimiz kerak.
\[f\left( x \right) = 2{x^2} + 13x - 7 = \left( {2x - 1} \right)\left( {x + 7} \right)\]Bundan bizda ikkita nol/ildiz borligini ko'ramiz: \(x = \frac{1}{2}\) va \(x = - 7\).
2-qadam
Ko'plik uchun shuni yodda tutingki, nol/ildizning ko'pligi shunchaki nol/ildiz hosil qiluvchi atamadagi ko'rsatkichdir. Shuning uchun, har bir nol/ildizning ko'paytmalari,
\[\begin{align*}x & = \frac{1}{2}:{\mbox{ multiplicity 1}}\\ x & = - 7:{\mbox{ multiplicity 1}}\end{align*}\]