F.5 A. Maths
2007-08-02 8:47 pm
a,b are the real roots of the equation x²+(k-2)x-(k-1)=0. If |a|=|b|, find k.
回答 (3)
2007-08-02 8:52 pm
✔ 最佳答案
As follows~~~圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/untitled15.jpg?t=1186030304
參考: Myself~~~
2007-08-02 11:12 pm
|a|=|b|
∴a=b or -b
when a=-b, sum of root =a+b=0
2-k=0
k=2
when a=b, sum of root =2a=2-k
product of root=a^2=-(k-1)=1-k
[(2-k)/2]^2=(1-k)
k^2-4k+4=4-4k
k^2=0
k=0
By combining the two cases, k=0 or 2
∴a=b or -b
when a=-b, sum of root =a+b=0
2-k=0
k=2
when a=b, sum of root =2a=2-k
product of root=a^2=-(k-1)=1-k
[(2-k)/2]^2=(1-k)
k^2-4k+4=4-4k
k^2=0
k=0
By combining the two cases, k=0 or 2
2007-08-02 9:08 pm
1)a=b
(k-2)^2+4(k-1)=0
k=0
2)a=-b
k-2=0
k=2
(k-2)^2+4(k-1)=0
k=0
2)a=-b
k-2=0
k=2
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