中視聶小倩線上看 , 聶小倩線上看第二集 , 聶小倩 中視 , 聶小倩電視劇 , 聶小倩

第一題：設 a, b, c 為整數, 且 a > b >0 , 若 x-c為 (x-a)(x-b)-5之因式,求a, b, c。

用因式定理, 即 (c-a)(c-b)-5 = 0
即 (c-a)(c-b) = 5
由於 a > b > 0, 所以 c-a < c-b
而且a, b, c 為整數
所以 (i) c-a =1 , c-b = 5
或 (ii) c-a =-5 , c-b = -1

(i) 決定 c 之後, a=c-1, b=c-5 即可
(ii) 決定 c 之後, a=c+5, b=c+1 即可

第二題：f(x)=(x-2)^5+ax+b有x-1和x-3兩個一次因式，求常數a, b。

f(1)=0 得 -1+a+b=0
f(3)=0 得 1+3a+b=0
所以 a = -1, b = 2

第三題：設多項式 f(x)滿足 f(x+2)-f(x)=4x-2，且f(0)=7，則f(1)=？

前明白 f(x) 為二次多項式（因為同次相減後為一次）。
設 f(x) = ax² + bx + c
f(0) = c = 7
f(x+2) = ax² + 4ax + 4a + bx + 2b + c
f(x+2) - f(x) = 4ax + 4a + 2b = 4x - 2
a = 1, b = -3
所以, f(x) = x² - 3x + 7
f(1) = 1-3+7 = 5

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