inequalities

For the equation 9x^2–(m+6)x+(m–2) = 0 having two unequal positive roots.
Discriminant = [-(m+6)]^2-4(9)(m-2) > 0
(m+6)^2-36(m-2) >0
m^2 + 12m + 36 - 36m + 72 >0
m^2–24 + 108 >0
(m–18)(m–6) > 0
m > 18 or m < 6 ...(1)

For both positive roots, sum of roots > 0 and Product of roots >0
i.e. (m+6)/9 > 0 and (m-2)/9>0
i.e. m > -6 and m > 2
m>2 ...(2)

Combining (1) and (2),
the solution is ** 2 < m < 6 or m > 18**

2007-10-12 23:43:27 補充：
問:點解要計sum of roots and Product of roots？ 答: 因為條題目emphasize "unequal positive roots"中的"positive"...所以一定要考慮兩根之和及兩根之積...若只提及"unequal roots",我們則只需考慮Discriminant > 0.這就是這條數的較深奧之處...不要忽略"positive"這字...問題中的每一隻字也是提示....