F.4 A.math 高手入

x^2-4x+k = 0 ...(1)
2x^2-3x+k = 0 ...(2)

(1)-(2),(α^2-4α+k)-(2α^2-3α+k)=0
α^2-4α+k-2α^2+3α-k=0
-α^2-α=0
α^2+α=0
α(α+1)=0
α=0 or α=-1

For the equation x^2-4x+k = 0,
when α=0,
0^2-4(0)+k=0
k=0
when α=-1,
-1^2-4(-1)+k=0
1+4+k=0
k=-5

For the equation 2x^2-3x+k = 0,
when α=0,
2(0)^2-3(0)+k=0
k=0
when α=-1,
2(-1)^2-3(-1)+k=0
2+3+k=0
k=-5

so,when α=0,k=0
when α=-1,k=-5

2008-10-03 15:54:55 補充：
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let the common root beα


α^2-4α+k=0-------1
2α^2-3α+k=0---------2

2-1,α^2+α=0
α=0,k=0 or
α=-1,k=-5