实数m为何值时关于x的方程7x²-(m+13)x+m²-m-2=0的两个实根x1,x2满足0
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![实数m为何值时关于x的方程7x²-(m+13)x+m²-m-2=0的两个实根x1,x2满足0](/uploads/image/z/1324851-51-1.jpg?t=%E5%AE%9E%E6%95%B0m%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%E5%85%B3%E4%BA%8Ex%E7%9A%84%E6%96%B9%E7%A8%8B7x%26%23178%3B-%EF%BC%88m%2B13%EF%BC%89x%2Bm%26%23178%3B-m-2%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%A0%B9x1%2Cx2%E6%BB%A1%E8%B6%B30)
实数m为何值时关于x的方程7x²-(m+13)x+m²-m-2=0的两个实根x1,x2满足0 实数m为何值时关于x的方程7x²-(m+13)x+m²-m-2=0的两个实根x1,x2满足0
实数m为何值时关于x的方程7x²-(m+13)x+m²-m-2=0的两个实根x1,x2满足0
此题应该这样求解,令f(x)=7x^2-(m+13)x+m^2-m-2
若两个实根满足0
即m^2-m-2>0,
28-2×(m+13)+m^2-m-2>0,
【4×7×(m^2-m-2)-(m+13)^2】/28<0
∴(3-2√21)/3
(m+13)^2-4*7(m^2-m-2)>0
m^2+26m+169-28m^2+28m+56>0
27m^2-54m-225<0
3m^2-6m-25<0
∴(3-2√21)/3