是x²-(4m-1)x-3m²=0吗?无论m取任何实数时,原方程总有两个实数根?
1、△=(4m-1)²+12m²
=14m²-8m+1+12m²
=28m²-8m+1
=28(m²-2/7m)+1
=28(m²-2/7m+1/49)+1-28/49
=28(m-1/7)²+1-4/7
=28(m-1/7)²+3/7>0
∴无论m取任何实数时,原方程总有两个实数根
是x²-(4m-1)x-3m²=0吗?无论m取任何实数时,原方程总有两个实数根?
1、△=(4m-1)²+12m²
=14m²-8m+1+12m²
=28m²-8m+1
=28(m²-2/7m)+1
=28(m²-2/7m+1/49)+1-28/49
=28(m-1/7)²+1-4/7
=28(m-1/7)²+3/7>0
∴无论m取任何实数时,原方程总有两个实数根