math:代数学の基本定理

# 差分

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 math:代数学の基本定理 [2017/01/21 ]N_Miya 作成 math:代数学の基本定理 [2017/01/21 ] (現在)N_Miya 2017/01/21 N_Miya 2017/01/21 N_Miya 作成 2017/01/21 N_Miya 2017/01/21 N_Miya 作成 ライン 8: ライン 8: Proof: Proof: - (1) Let f(x) = xn + a1xn-1 + ... + an-1x + an + (1) Let f(x) = x^n + a1x^(n-1) + ... + an-1x + an (2) Let α be a root such that f(α) = 0 (2) Let α be a root such that f(α) = 0 ライン 32: ライン 32: For any polynomial equation of order n, there exist n roots ri such that: For any polynomial equation of order n, there exist n roots ri such that: - xn + a1xn-1 + ... + an-1x + an = (x - r1)(x - r2)*...*(x - rn) + x^n + a1x^(n-1) + ... + an-1x + an = (x - r1)(x - r2)*...*(x - rn) Proof: Proof: - (1) Let f(x) = xn + a1xn-1 + ... + an-1x + an + (1) Let f(x) = x^n + a1x^(n-1) + ... + an-1x + an (2) We know that f(x) has at least one solution α1. [See here for proof] (2) We know that f(x) has at least one solution α1. [See here for proof]
math/代数学の基本定理.txt · 最終更新: 2017/01/21 by N_Miya