Question

设函数f(x)=f(2)x^2+f(1)x+f(0),已知方程f(x)=x有一个大于2的根,求f(0)的范围

Answer 1

f(1) = f(2) + f(1) +f(0) ,所以,f(2) = - f(0)f(2) = -f(0) 4 + f(1) 2 +f(0) = - f(0) ,所以,f(1) = f(0)所以,函数 f(x) = -f(0)x^2 + f(0)x + f(0),由 f(x) = x 得 f(0) = x / (-x^2 + x + 1),联立 x>2得 f(0) > ...