中四 A MATHS 二次方程一問~

x^2-4x+k=0 and 2x^2-3x+k=0 have a same root α
i.e. α^2-4α+k=0 and 2α^2-3α+k=0
then , α^2-4α+k=2α^2-3α+k
α^2+α=0
α=0 or α=-1 ,

then put α=0 into x^2+4x+k=0 , then k=0
put α=-1 into x^2+4x+k=0 , k=3

so k=0 or k=3//

Sub A to both of the equations

A^2-4A+k=0 and
2A^2-3A+k=0

Then
A^2-4A+k=2A^2-3A+k
A=0 or -1

When A=0, k=0
When A=-1, k=-5

他應該計錯，答案應是０／－５。
他用的方法可參考^O^