let g(x)=2x^3+mx^2+10x+n,where m and n are constants.2x-1 and x-3 are
factors of g(x).
a)find the values of m and n.
b)factorize g(x).
f4 polynomial!!!
2010-02-21 9:33 pm
回答 (2)
2010-02-21 9:58 pm
✔ 最佳答案
a)g(1/2)=0
2(1/2)3+m(1/2)2+10(1/2)+n=0
1/4+1/4m+5+n=0
1/4m+n=-21/4_______________________________________(1)
g(3)=0
2(3)3+m(3)2+10(3)+n=0
54+9m+30+n=0
9m+n=-84__________________________________(2)
解(1)和(2),可得:
m=-9及n=-3
b)
g(x)= 2x3-9x2+10x-3
=(x-3)(x-1)(2x-1)
2010-02-21 9:59 pm
sub x=1/2
2(1/2)^3+(1/2)^2m+10(1/2)+n=0
1/4+1/4m+5+n=0
21/4+1/4+n=0 ------------1
sub x=3
2(3^3)+9m+30+n=0
54+9m+30+n=0
84+9m+n=0 ---------2
2-1
35/4m=315/4
m=9
sub m=9 into 2
84+9(9)+n=0
n=-3
g(x)=2x^3+9x^2+10x-3
g(x)=(2x-1)(x-3)(x-1)
2(1/2)^3+(1/2)^2m+10(1/2)+n=0
1/4+1/4m+5+n=0
21/4+1/4+n=0 ------------1
sub x=3
2(3^3)+9m+30+n=0
54+9m+30+n=0
84+9m+n=0 ---------2
2-1
35/4m=315/4
m=9
sub m=9 into 2
84+9(9)+n=0
n=-3
g(x)=2x^3+9x^2+10x-3
g(x)=(2x-1)(x-3)(x-1)
收錄日期: 2021-04-23 20:40:03
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100221000051KK00700