if roots of equation 2x^2+(m-4)x+m+2=0 are both negative,find range of values of m
A.m</-一2 or m>/16
b.0</m<4
c) -2<m</0 or m>/16
d.-2<m<4 or m>/16
我想問點解我用計數機代入條formula~~發覺abcd的答案都唔岩
例如m=-3~~~A唔岩
M=2~~B唔岩
M=-1~~~CD都唔岩的???
math problem
2012-06-29 10:53 pm
回答 (1)
2012-07-03 7:22 pm
✔ 最佳答案
2x² + (m - 4)x + m + 2 = 0 have both negative roots=> Δ > 0 and sum of roots < 0 and product of roots > 0
=> (m - 4)² - 4(2)(m + 2) > 0 and -(m - 4) / 2 < 0 and (m + 2) / 2 > 0
=> m² - 8m + 16 - 8m - 16 > 0 and -(m - 4) < 0 and m + 2 > 0
=> m² - 16m > 0 and m - 4 > 0 and m + 2 > 0
=> (m < 0 or m > 16) and m > 4 and m > -2
=> m > 16
therefore, the question has some mistakes, the answer should be m > 16
參考: knowledge
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120629000051KK00315