8.若函数y=(k²-1)x²+(k-1)x+2的值域为非负实数,求实数k的取值范围
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![8.若函数y=(k²-1)x²+(k-1)x+2的值域为非负实数,求实数k的取值范围](/uploads/image/z/11507395-67-5.jpg?t=8.%E8%8B%A5%E5%87%BD%E6%95%B0y%3D%EF%BC%88k%26%23178%3B-1%EF%BC%89x%26%23178%3B%2B%EF%BC%88k-1%EF%BC%89x%2B2%E7%9A%84%E5%80%BC%E5%9F%9F%E4%B8%BA%E9%9D%9E%E8%B4%9F%E5%AE%9E%E6%95%B0%2C%E6%B1%82%E5%AE%9E%E6%95%B0k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
8.若函数y=(k²-1)x²+(k-1)x+2的值域为非负实数,求实数k的取值范围
8.若函数y=(k²-1)x²+(k-1)x+2的值域为非负实数,求实数k的取值范围
8.若函数y=(k²-1)x²+(k-1)x+2的值域为非负实数,求实数k的取值范围
y=(k²-1)x²+(k-1)x+2的值域为非负实数抛物线开口向上,即(k²-1)≥0,在此推出k≥1或k≤-1
y=(k²-1)x²+(k-1)x+2的值域为非负实数,即(k-1)²-4(k²-1)=0,解出k=1,k=-5/3
两个答案相交得k=1,k=-5/3
k>=1,k<-1