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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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請問一下有關數學多項式的問題?
Jul 31st 2014, 09:32

f(x)=x^4+ax^2+bx+2(x1)^2整除,則2a+3b=?
Sol
f(x)=x^4+ax^2+bx+2
f’(x)=4x^3+2ax+b
f(1)=1+a+b+2=0
f’(1)=4+2a+b=0
(4+2a+b)
(1+a+b+2)=0
a=
1b=2
or
        x2+2x+2
       ─────────────────
x2-2x+1)x4+ax2+bx+2
       )x4-2x3+x2
       )────────────────
       )2x3+(a-1)x2+bx+2
       )2x3-4x2+2x
       )────────────────
       )(a+3)x2+(b-2)x+2
       )    2x2-    4x+2
       )────────────────
       )0
So
a=
1b=2

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