2道英文的数学题,

题目

2道英文的数学题,
1)If f (x) = ax^2 + bx + c; f (2012) = 0; f (2010) = 0 and f (0) = 8,088,240
then for what value of x is f a maximum?What is the maximum value of f
2)What is the remainder when2011x^2010+ 2009x^1005+ 2005x^201+ 2003x^67
+ 2001 is divided by x + (Don’t use synthetic division!)

答案

1 x=2011 f(x)取到最值
由韦达定理,-b/a=4022 c/a=4044120
c=f(0)=8088240
所以a=2 b=-8044
最小值fmin=f(2011)=2(2011-2012)(2011-2010)=-2
2 将x=-1带入,原式=2011-2009-2005-2003+2001=-2005
所以原式加上2005后,就含有因式x+1
又因为原式除以x+1的结果必然是一个常数,所以这个常数是-2005,这就是余数