Pure Maths --- Polynomial
2008-07-16 2:51 am
圖片參考：http://hk.geocities.com/stevieg_1023/02.gif
我想問下bii part....我唔用佢上邊個d方法,我個做法係:
let f(x)=2x^3+3x^2+x+c
f'(x)=6x^2+6x+1
let f'(x)=0
咁計到令f'(x)=0的x值....
將佢代番去f(x)度...求番個C......呢個做法得唔得?
[因為若f(x)=0 has a repeated root if and only if f(x0)=f'(x0)=0 for some x0]
回答 (1)
2008-07-16 7:46 am
✔ 最佳答案
可以, 因為既然:f(x)=0 has a repeated root if and only if f(x0)=f'(x0)=0 for some x
"if and only if" 係雙向的關係, 所以, 只要:
2x03 + 3x02 + x0 + c = 0 and 6x02 + 6x0 + 1 = 0, 如此:
2x3 + 3x2 + x + c = 0 has a repeated root.
So to give a positive c, x0 = (- 3 + √3)/6 and hence c = (√3)/18
參考: My Maths knowledge
收錄日期: 2021-04-22 00:33:41
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080715000051KK02370