Question

设P(x)=x^4+ax^3+bx^2+cx+d,其中a、b、c、d为常数,如果P(1)=10,P(2)=20,P(3)

Answer 1

设F(x)=f(x)-10x ∴F(1)=F(2)=F(3)=0 ∴F(x)=(x-1)(x-2)(x-3)(x+h) f(x)=F(x)+10x f(10)=F(10)+100=9*8*7*(10+h)+100 f(-6)=F(-6)-60=-7*8*9(-6+h)-60 f(10)+f(-6)=10*9*8*7+9*8*7h+100+6*7*8*9-7*8*9h-60 =5040+3024+100-60 =8104