搜搜考试网有关函数的数学题求解答.（题目是英文的）.
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有关函数的数学题求解答.（题目是英文的）.
The polynomial f(x)=ax^4-2x^3+bx^2+2x has a factor of (x+1) and has a stationary value at x=1/2.Find the value of a and of b.
The polynomial f(x)=ax^4-2x^3+bx^2+2x has a factor of (x+1) and has a stationary value at x=1/2.Find the value of a and of b.
应该可以用中文回答的吧,需要英文版追问我.
先求导f'(x)=4ax^3-6x^2+2bx+2
有因式（x+1）,即当x=-1,f(-1)=0=a+2+b-2=a+b (1)
当x=1/2时有极值,即f'(1/2)=0=4a*1/8-6*1/4+2b*1/2+2=a/2-3/2+b+2=0 (2)
由方程（1）（2）列方程组,即可解得a=1,b=-1
先求导f'(x)=4ax^3-6x^2+2bx+2
有因式（x+1）,即当x=-1,f(-1)=0=a+2+b-2=a+b (1)
当x=1/2时有极值,即f'(1/2)=0=4a*1/8-6*1/4+2b*1/2+2=a/2-3/2+b+2=0 (2)
由方程（1）（2）列方程组,即可解得a=1,b=-1