方程x2+(m-2)x+5-m=0的两根都大于2,则m的取值范围是( ) A.(-5,-4] B.(-∞,-4] C.(-∞,-2] D.(-∞,-5)∪(-5,-4]
问题描述:
方程x2+(m-2)x+5-m=0的两根都大于2,则m的取值范围是( )
A. (-5,-4]
B. (-∞,-4]
C. (-∞,-2]
D. (-∞,-5)∪(-5,-4]
答
令f(x)=x2+(m-2)x+5-m,其对称轴方程为x=2−m2 由已知方程x2+(m-2)x+5-m=0的两根都大于2,故有2−m2>2f(2)>0△≥0 即2−m2>24+2m−4+5−m>0(m−2) 2−4(5−m)≥0解得-5<m≤-4 ...