方程x²+k(x-1)-x=0可化为 x²+(k-1)x-k=0
(1)∵b²－4ac
=(k-1)²－4×1×(-k)
=k²-2k+1+4k
=k²+2k+1
=(k+1)²≥0
∴不论k取何值,方程一定有实数根.
(2)将x=½√3代入x²+(k-1)x-k=0,得
¾+(k-1)×(½√3)-k=0
解得：k=(9-4√3)/11.