Question

设函数f(x)=x^2+ax+b,集合={xIf(x)=x}={a},求a,b的值

Answer 1

f(x)=x^2+ax+b,A={x|f(x)=x}={a},

x=f(x)

x=x^2+ax+b

x^2+(a-1)x+b=0

for double roots a

(x-a)^2 =0

x-2ax+a^2=0

compare coefficient of x,constant

=> a-1 =-2a

a= 1/3 #

b=a^2 = 1/9 #