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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
設f(x)=x^4+ax^2+bx+2被(x-1)^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=-1,b=-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=-1,b=-2
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