1. s,k,t 為整數 (x-s)(x-10)+1=(x-k)(x-t) 求(s,k,t )=
Ans:(12,11,11) or (8,9,9)
2. f(x)為實係數多項式,且f(2)=f(6)>f(3)=f(5)
f(x)除以(x-2)(x-3)(x-5)(x-6)的餘式為r(x),則下列哪些可能是
r(x)?
(A) 7 (B) 7X+3 (C) -X^2+8X+5 (D) x^2-8x+9 (E) -3x^2+24x+9
感謝
函數2題(謝謝老師)
版主: thepiano
Re: 函數2題(謝謝老師)
第 1 題
s + 10 = k + t
10s + 1 = kt
10(k + t - 10) + 1 = kt
......
第 2 題
f(2) = r(2)，f(6) = r(6)，f(3) = r(3)，f(5) = r(5)
r(2) = r(6) ＞ r(3) = r(5)
......
s + 10 = k + t
10s + 1 = kt
10(k + t - 10) + 1 = kt
......
第 2 題
f(2) = r(2)，f(6) = r(6)，f(3) = r(3)，f(5) = r(5)
r(2) = r(6) ＞ r(3) = r(5)
......
Re: 函數2題(謝謝老師)
kt - 10k - 10t = -99
kt - 10k - 10t + 100 = 1
(k - 10)(t - 10) = 1
k - 10 = 1，t - 10 = 1 or k - 10 = -1，t - 10 = -1
kt - 10k - 10t + 100 = 1
(k - 10)(t - 10) = 1
k - 10 = 1，t - 10 = 1 or k - 10 = -1，t - 10 = -1