假设存在m∈R,使得f(m)=-a成立时,f(m+3)为正数
由题意得
a+b+c=0
m^2a+mb+c=-a
联立用m,a表示b,c得
b=m^2/(1-m)*a
c=-(m^2-m+1)/(1-m)*a
代入f(x)
f(x)=ax^2+m^2/(1-m)*ax-(m^2-m+1)/(1-m)*a
则
f(m+3)
=a(m+3)^2+m^2(m+3)/(1-m)*a-(m^2-m+1)/(1-m)*a
=(m+2)(3m-4)/(m-1)*a
因为a不等于0
1当a>0时,使f(m+3)>0即(m+2)(3m-4)/(m-1)*a>0即使(m+2)(3m-4)/(m-1)>0
解得-20即使(m+2)(3m-4)/(m-1)