∆ = (8m+1)² -4*4*4m² = 16m + 1 ≥ 0,m ≥ -1/16
但m≠0,否则方程不成立
(1) 设二根为p,q
1/p + 1/q = (p+q)/(pq)
= [-(8m+1)/(4m²)]/[4/(4m²)] = -(8m+1)/4 ≤ -2
8m + 1 ≥ 8
m ≥ 7/8
与前提不矛盾
(2)设二根为p,4p
方程可变为:4m²(x -p)(x-4p) = 0
4m²x² - 20pm²x +16p²m² = 0
比较系数:-20pm² = 8m+1
16p²m² = 4
解得m = 1/2或m = -1/18,
与前提不矛盾