推 tml :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
→ tml :P'(a)=6x^2+14x+k=0,k=-(6x^2+14x)代回得 11/21 00:12
→ tml :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
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.
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