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x^4+2x^3+2x^2+10x+25=0
令x^4+2x^3+2x^2+10x+25=(x^2+ax+b)(x^2+cx+d)
=
=x^4+(c+a)x^3+(d+b+ac)x^2+(ad+bc)x+bd
比較係數知:
c+a=2,d+b+ac=2,ad+bc=10, bd=25
令b=d=5
==>a+c=2, ac=-8 視如解x^2-2x-8=0的解x=4,-2
==>a=4,c=-2或a=-2,c=4
x^4+2x^3+2x^2+10x+25=0
==>(x^2-2x+5)(x^2+4x+5)=0
==>x=-2-i,-2+i,1-2i,1+2i
本文出自: http://tw.knowledge.yahoo.com/question/question?qid=1012042301320
令x^4+2x^3+2x^2+10x+25=(x^2+ax+b)(x^2+cx+d)
=
=x^4+(c+a)x^3+(d+b+ac)x^2+(ad+bc)x+bd
比較係數知:
c+a=2,d+b+ac=2,ad+bc=10, bd=25
令b=d=5
==>a+c=2, ac=-8 視如解x^2-2x-8=0的解x=4,-2
==>a=4,c=-2或a=-2,c=4
x^4+2x^3+2x^2+10x+25=0
==>(x^2-2x+5)(x^2+4x+5)=0
==>x=-2-i,-2+i,1-2i,1+2i
本文出自: http://tw.knowledge.yahoo.com/question/question?qid=1012042301320
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