当m为何值时,方程2x²-(4m+1)x+2m²-1=0 (1)有两个不相等的实数根?(2)有两个相等的实数根?(3)没有实数根?
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![当m为何值时,方程2x²-(4m+1)x+2m²-1=0 (1)有两个不相等的实数根?(2)有两个相等的实数根?(3)没有实数根?](/uploads/image/z/963070-70-0.jpg?t=%E5%BD%93m%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E6%96%B9%E7%A8%8B2x%26%23178%3B-%EF%BC%884m%2B1%EF%BC%89x%2B2m%26%23178%3B-1%3D0+%EF%BC%881%EF%BC%89%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%3F%EF%BC%882%EF%BC%89%E6%9C%89%E4%B8%A4%E4%B8%AA%E7%9B%B8%E7%AD%89%E7%9A%84%E5%AE%9E%E6%95%B0%E6%A0%B9%3F%EF%BC%883%EF%BC%89%E6%B2%A1%E6%9C%89%E5%AE%9E%E6%95%B0%E6%A0%B9%3F)
当m为何值时,方程2x²-(4m+1)x+2m²-1=0 (1)有两个不相等的实数根?(2)有两个相等的实数根?(3)没有实数根?
当m为何值时,方程2x²-(4m+1)x+2m²-1=0 (1)有两个不相等的实数根?
(2)有两个相等的实数根?
(3)没有实数根?
当m为何值时,方程2x²-(4m+1)x+2m²-1=0 (1)有两个不相等的实数根?(2)有两个相等的实数根?(3)没有实数根?
∵a=2,b=-(4m+1),c=2m²-1
△=b²-4ac=[-(4m+1)]²-4×2×(2m²-1)=8m+9
(1)当△>0时有两具不相等的实数根
即8m+9>0
m>-9/8
(2)当△=0时有两具相等的实数根
即8m+9=0
m=-9/8
(3)当△<0时没有实数根
即8m+9<0
m<-9/8
△=(4m+1)2-8(2m2-1) =8m+9(1)△>0 m>-8/9(2)△=0 m=-8/9(3)△<0 m<-8/9
由△=b^2-4ac得
△=(4m+1)^2-4*2*(2m^2-1)=8m+9
当△>0时有两个不相等的实数根,m>-9/8
当△=0时有两个相等的实数根,m=-9/8
当△<0时有没有实数根,m<-9/8