[中學] 怎麼假設比較好運算

看板Math作者 ( 由心出發 )時間12年前 (2013/11/20 23:45), 編輯推噓1(1推 0噓 2→)
留言3則, 1人參與, 最新討論串1/2 (看更多)
http://ppt.cc/CPL1 如圖 11. P(x)=2x^3+7x^2+kx-k is the product of 3 liner factors, 2 of which are identical. a.Show that k can take 3 distinct values. b.Write P(x) as the product of linear factors for the case where k is greatest. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.38.246.147
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11/21 00:11, , 1F
不限中學的話微分比較好算,假設a為重根P(a)=P'(a)=0
11/21 00:11, 1F
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11/21 00:12, , 2F
P'(a)=6x^2+14x+k=0,k=-(6x^2+14x)代回得
11/21 00:12, 2F
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11/21 00:13, , 3F
P(a)=-4a^3-a^2+14a=0,解得a=0,-2,7/4分別代回可得k
11/21 00:13, 3F
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文章代碼(AID): #1IZDasgW (Math)