5.2-bo'lim : ko'phadlarning nollari/ildizlari
3. Quyidagi ko‘phadning barcha nollarini sanab bering va ularning ko‘paytmalarini keltiring.
\[\begin{align*}A\left( x \right) & = {x^8} + 2{x^7} - 29{x^6} - 76{x^5} + 199{x^4} + 722{x^3} + 261{x^2} - 648x - 432\\ & = {\left( {x + 1} \right)^2}{\left( {x - 4} \right)^2}\left( {x - 1} \right){\left( {x + 3} \right)^3}\end{align*}\]Yechim
Bu muammo uchun ko'phad allaqachon faktorlarga ajratilgan va shuning uchun biz qilishimiz kerak bo'lgan narsa faktorlangan shakldan nol/ildizlarni olishdir.
Bu ko'phadning nollari/ildizlari: \(x = - 1\), \(x = 4\), \(x = 1\) va \(x = - 3\).
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,
\[\begin{align*}& x = - 1:{\mbox{ multiplicity 2}}\\ & x = 4:{\mbox{ multiplicity 2}}\\ & x = 1:{\mbox{ multiplicity 1}}\\ & x = - 3:{\mbox{ multiplicity 3}}\end{align*}\]