Question

已知函数f(x)=ax^2+bx+c. 满足f(1)=0,且a>b>c. 求c/a的取值范围

Answer 1

好长时间没做了a+b+c=0,a>b>c,得a>0,c<0,a>b>-a,-1<b/a<1,c/a=-1-b/a,-2<c/a<0

Answer 2

f(1)=0

a+b+c=0

1° b>0
a+b=-c
2a>-c
c/a<-2

2° b≤0
b+c=-a
2c≤-a
c/a<-1/2

c/a<-1/2