Amaths~inequality

2008-10-07 10:20 pm
ax^2+bx+c>0
咁a>0~佢就係opening upward
a<0就係opening downward
而△>0就係有real roots
△=0就係有一個real root
△<0就係無real root
應該無錯啦可........

咁而家有條數係
find the range of real values of k if kx^2+(4k-1)x+4k(>=)0 for all real values of k.
咁因為k唔知係+ 定-
咁我咪要分case做既
咁我咁做岩唔岩??
Case1 k>0
△(>=)0 (因為all real values of k)
(4k+1)^2-4(k)(4k)(>=)0
k(<=)1/8

Case2 k<0
△(>=)0 (因為all real values of k)
(4k+1)^2-4(k)(4k)(>=)0
k(<=)1/8
(rejected) (因為k<0)

但係個答案係k(>=)1/8
點解會咁既...我做錯左D咩...=3="

仲有~有時知道左個graph點畫咁又可以點幫我計數??
同埋~例如
有時咪要consider y=ax^2+bx+c=0先計既
咁係幾時要幾時就可以(ax^2+bx+c>0)咁樣直接計??

用中文~詳盡D~最好有解釋~
但唔好太深...因為岩岩先學...有好多都唔明...> <"
最慘係唔明自已唔明D咩...=3="""
唔該~=]
更新1:

但係~ -8k(>=)-1 乘除-數唔係要掉符號嫁咩?? mm...例如~ ax^2+bx+c>0 唔係要consider y=ax^2+bx+c=0 之後先可以用ax^2+bx+c=0黎計嫁咩?? 係咩情況下計要consider 係咩情況下計就直接ax^2+bx+c>0?? 咁講會唔會好D??

回答 (2)

2008-10-07 11:11 pm
✔ 最佳答案
你係過程到做錯左
△(>=)0 (因為all real values of k)
(4k+1)^2-4(k)(4k)(>=)0
16k^2-8k+1-16k^2(>=)0
-8k(>=)-1
SO k(>=)1/8

個GRAPH唔係叫係去計數
而是叫你'睇',個ANS

你個例子我睇唔明
可以詳細D嗎?

你唔明睇多D
我都係剛剛教左
希望幫到你
參考: me
2008-10-08 1:46 am
For a quadratic function to be always positive (that is > 0), that means the function will never touch the x-axis. For a function never touch the x-axis, its delta must be smaller than zero( that is negative). That is b^2 - 4ac < 0.
For this question, delta = -8k + 1< 0
So 1 < 8k
k> 1/8.
Since the function = 0 is also acceptable, therefore k can also be = 1/8.
(Note: 001 said -8k > -1, then 8k > 1 is not correct because the sign must be reversed if you multiply both side by -1.)


收錄日期: 2021-04-25 22:35:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081007000051KK01191

檢視 Wayback Machine 備份