试证明:不论M为何值,方程2x²-(4m-1)x-m²=0总有两个不相等的实数根.(快!)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 17:59:03
![试证明:不论M为何值,方程2x²-(4m-1)x-m²=0总有两个不相等的实数根.(快!)](/uploads/image/z/2674045-37-5.jpg?t=%E8%AF%95%E8%AF%81%E6%98%8E%EF%BC%9A%E4%B8%8D%E8%AE%BAM%E4%B8%BA%E4%BD%95%E5%80%BC%2C%E6%96%B9%E7%A8%8B2x%26%23178%3B-%EF%BC%884m-1%29x-m%26%23178%3B%3D0%E6%80%BB%E6%9C%89%E4%B8%A4%E4%B8%AA%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84%E5%AE%9E%E6%95%B0%E6%A0%B9.%28%E5%BF%AB%21%29)
试证明:不论M为何值,方程2x²-(4m-1)x-m²=0总有两个不相等的实数根.(快!)
试证明:不论M为何值,方程2x²-(4m-1)x-m²=0总有两个不相等的实数根.(快!)
试证明:不论M为何值,方程2x²-(4m-1)x-m²=0总有两个不相等的实数根.(快!)
证明:
判别式
Δ=(4m-1)²-4*2*(-m²)
=(4m-1)²+8m²
=16m²-8m+1+8m²
=24m²-8m+1
=24(m²-m/3+1/36-1/36)+1
=24(m-1/6)²-2/3+1
=24(m-1/6)²+1/3>0
所以方程2x²-(4m-1)x-m²=0总有两个不相等的实数根