51问答网 > 已知关于x的一元二次方程kx2-2（k+1）x+k-1=0有两个不相等的实数根x1，x2．（1）求k的取值范围；（2）是

已知关于x的一元二次方程kx2-2（k+1）x+k-1=0有两个不相等的实数根x1，x2．（1）求k的取值范围；（2）是

2025-03-14 06:11:55
推荐回答（1个）
回答1：

（1）由题意知，k≠0且△=b2-4ac＞0
∴b2-4ac=[-2（k+1）]2-4k（k-1）＞0，
即4k2+8k+4-4k2+4k＞0，
∴12k＞-4
解得：k＞-
1
3
且k≠0

（2）不存在．
∵x1+x2=
2(k+1)
k
，x1?x2=
k?1
k
，
又有
1
x1
+
1
x2
=
x1+x2
x1x2
=1，
可求得k=-3，而-3＜-
1
3

∴满足条件的k值不存在．

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