mathematics

2007-06-29 8:29 pm
已知f(x)=8x^3 +ax+ b可被2x-1和2x+1整除,求a的值。

回答 (2)

2007-06-29 8:34 pm
✔ 最佳答案
2x-1 and 2x +1 are factor of f(x)

=> f(1/2) and f(-1/2) both = 0

f(1/2) = 8(1/2)^3 + a/2 + b = 0 = 1 + a/2 +b (eq1)
f(-1/2) = 8(-1/2)^3 - a/2 + b = 0 = -1 - a/2 + b (eq2)

eq1-eq2

(1+a/2+b)-(-1-a/2+b)=0
2+a=0
a=-2
2007-06-29 8:36 pm
f(0.5)= 8 X 0.5 3 + 0.5a + b =0
1+0.5a+b=0
f(-0.5)= 8 X -0.5 3 -0.5a + b =0
-1-0.5a+b=0
2+a=0
a=-2


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