关于余数定理和因式定理的数学题!急急急急急急急急急!!!翻译过来的不好意思~请清楚列出这两题的做法

2024-12-03 01:51:27
推荐回答(1个)
回答1:

设f(x) = 2x² + 6x + 3,余数为r
则-p及2q是下列方程式
2x^2 + 6x + 3 = r
的两个解
2x^2 + 6x + 3 - r = 0
两根之和 = -(6)/(2)
-p + 2q = -3
p - 2q = 3
===================================
f(a) = a^3 - ba^2 - 4b^2 a + 4b^3
f(2b) = (2b)^3 - b(2b)^2 - 4(b^2)(2b) + 4b^3
= 8b^3 - 4b^3 - 8b^3 + 4b^3
= 0
f(a)有因式(a-2b)(得证)
====================================
f(-b) = (-b)^3 - b(-b)^2 - 4(b^2)(-b) + 4b^3
= -b^3 -b^3 + 4b^3 + 4b^3
= 6b^3