由 gkw0824usa 於 星期二 一月 16, 2007 2:01 pm
#ed_op#DIV#ed_cl#By Vieta's formula, we know that there must exist a factor that is x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-2x+a,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#therefore we can let the factors of the initial equation be#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-2x+a#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# x ) x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+bx+c #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#STRIKE#ed_cl# #ed_op#/STRIKE#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#1. We know that the coefficient of x#ed_op#SUP#ed_cl#3#ed_op#/SUP#ed_cl# is 0,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# therefore, b-2=0 → b=2.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#2. We know that the coefficient of x#ed_op#SUP#ed_cl#2 #ed_op#/SUP#ed_cl#is -10,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# hence, a+c-2b=-10 → a+c=-6#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#3. We know that the coefficient of x is 8,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# thus -2c+ab=8 → a-c=4#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#4. By a+c=4, a-c=4 we know a=-1, c=-5#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# therefore, k=ac=5#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#5. By those above, we could find out:#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#initial equation#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#→(x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-2x-1)(x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+2x-5)=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#IMG alt="image file name: 2k957475bdb4.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2k957475bdb4.gif" border=0#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#Thanks, I've corrected it#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#