f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0,0),(x1,0),(x2,0),且f(x)在x=1,x=2时取极值,则x1*x2

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f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0,0),(x1,0),(x2,0),且f(x)在x=1,x=2时取极值,则x1*x2f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0

f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0,0),(x1,0),(x2,0),且f(x)在x=1,x=2时取极值,则x1*x2
f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0,0),(x1,0),(x2,0),且f(x)在x=1,x=2时取极值,则x1*x2

f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0,0),(x1,0),(x2,0),且f(x)在x=1,x=2时取极值,则x1*x2
首先,求导,f'(x)=3ax^2+2bx+c.
因为x=1,x=2时取极值,故f'(1)=0,f'(2)=0
所以,f'(1)=3a+2b+c=0(1)
f'(2)=12a+4b+c=0(2)两式想减,得9a+2b=0,故b=-9a/2 (3)
代人(1)得c=-3a-2b=6a
又因为,f(x)=ax^3+bx^2+cx+d与x轴有三个交点(0,0),(x1,0),(x2,0),即过(0,0),代入,得d=0
故f(x)=ax^3+bx^2+cx =ax^3-(9a/2) x^2+6ax =x(ax^2-(9a/2) x+6a )
而 x1,x2一定是ax^2-(9a/2) x+6a =0的两根,所以两根之积x1*x2 =(6a)/a=6
打出来这些,真是好费劲啊……希望你能看懂,我写的挺详细了