已知f(x)=x^2+(lga+3)x+lgb,且f(-1)=-3,f(x)>=3x,求a.b的值?

题目

已知f(x)=x^2+(lga+3)x+lgb,且f(-1)=-3,f(x)>=3x,求a.b的值?

答案

f(-1)=-3
-3=1-(lga+3)+lgb
lga=1+lgb
f(x)=x^2+(lga+3)x+lgb>=3x
x^2+lgax+lgb>=0
x^2+(1+lgb)x+lgb>=0
(x+lgb)(x+1)>=0
lgb=1,b=10,a=100