1. 設n次函數f(x)=(x-1)(x-2)(x-3)g(x)+ax^2+bx+c
x=1 帶入f(x), 得 f(1)=a+b+c=5..........(1)
x=2 帶入f(x), 得 f(2)=4a+2b+c=3......(2)
x=3 帶入f(x), 得 f(3)=9a+3b+c=7......(3)
將(1),(2),(3)聯立 , 得a=3,b=-11,c=13
f(x)除以(x-1)(x-2)(x-3)的餘式為 3x^2-11x+13
2.f(x)=(x^2+x-2)g(x)+2x+3
=(x+2)(x-1)g(x)+2x+3
f(1)=5, f(-2)=-1
f(x)=(x^2-x-6)h(x)+3x+a
=(x-3)(x+2)h(x)+3x+a
因f(-2)=-1, 3(-2)+a=-1 , a=5
則f(x)=(x-3)(x+2)h(x)+3x+5
x=3帶入f(x), f(3)=14
f(x)=(x^2+x-12)r(x)+4x+b
=(x+4)(x-3)r(x)+4x+b
x=3帶入f(x) , f(3)=4*3+b=14 , b=2
a=5,b=2
This entry passed through the Full-Text RSS service - if this is your content and you're reading it on someone else's site, please read the FAQ at fivefilters.org/content-only/faq.php#publishers.
留言列表
留言列表