f.4 a.math

2007-01-02 5:37 am
If the quadratic equation x^2+(m+2)x+(m+5)=0 has two unequal positive real roots,find the range of real values of m.
更新1:

how to combine??

回答 (2)

2007-01-02 5:42 am
✔ 最佳答案
consider discriminant
discriminant
=(m+2)^2-4(m+5)
=m^2+4m+4-4m-20
=m^2-16
=(m+4)(m-4)
Since the quadratic equation x^2+(m+2)x+(m+5)=0 has two unequal positive real roots
(m+4)(m-4)>0
-4<m<4
Also the sum and product of two unequal positive real roots>0
we have
-(m+2)>0
m+2<0
m<-2
m+5>0
m>-5
Combine all result
-4<m<-2


2007-01-01 21:47:39 補充:
攪錯(m+4)(m-4)&gt;0這裡是m&lt;-4 or m&gt;4Combine all result-5&lt;-4

2007-01-01 21:48:36 補充:
-5 less than m less than -4

2007-01-02 00:21:30 補充:
m less than 4 or m greater than 4 (1)m less than -2 (2)m greater than -5 (3)這些是and 條件combine 埋一齊便成

2007-01-02 00:21:53 補充:
m less than -4 or m greater than 4 (1)
2007-01-02 5:40 am
收la唔明


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