x^3 +5x^2+ax+2= (x^2-1)(x+5)-2x+b ,Find a and b
At last I get
ax+3x=b-7
Why b=7 and a=-3?
Also
when 3x^3-16x^2+ax+b is divided by (x-1)(x-3), the reminder is x+2.How can I find the values of a and b?
F4 mth
2010-12-04 11:03 pm
回答 (2)
2010-12-04 11:13 pm
✔ 最佳答案
Question 1x^3 +5x^2+ax+2= (x^2-1)(x+5)-2x+b
x^3 +5x^2+ax+2= x^3+5x^2-3x+b-5
Comparing corresponding coefficients,a=-3,b=7.
Question 2
3x^3-16x^2+ax+b=(x-1)(x-3)Q(x)+x+2
Sub. x=1 and 3 respectively
3-16+a+b=3
81-144+3a+b=5
Solve it a=26 b=-10
2010-12-04 11:27 pm
1
x^3 +5x^2+ax+2= (x^2-1)(x+5)-2x+b
= x^3+5x^2-3x+(b-5)
by comparing the coefficients,
a=-3 , b=7
2
3x^3-16x^2+ax+b=(x-1)(x-3)Q(x)+x+2 where Q= Ax+B
=(x-1)(x-3)(Ax+B)+x+2
=Ax^3+(B-4A)x^2 +(3A-4B+1)x+3B+2
by comparing the coefficient
A=3, B-4A=-16, 3(3)-4(-4)+1=a=26, b=3(-4)+2=-10
B=-4
x^3 +5x^2+ax+2= (x^2-1)(x+5)-2x+b
= x^3+5x^2-3x+(b-5)
by comparing the coefficients,
a=-3 , b=7
2
3x^3-16x^2+ax+b=(x-1)(x-3)Q(x)+x+2 where Q= Ax+B
=(x-1)(x-3)(Ax+B)+x+2
=Ax^3+(B-4A)x^2 +(3A-4B+1)x+3B+2
by comparing the coefficient
A=3, B-4A=-16, 3(3)-4(-4)+1=a=26, b=3(-4)+2=-10
B=-4
收錄日期: 2021-04-23 20:42:43
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101204000051KK00710