已知二次函数f(x)=ax2+bx+c.
1个回答

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

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)