Inequality

So to speak:

3x2 + (2 +k)x + 3k - 18 = 0 has no real roots and so:

(2 + k)2 - 4 x 3 (3k - 18) < 0

k2 + 4k + 4 - 36k + 216 < 0

k2 - 32k + 220 < 0

(k - 10)(k - 22) < 0

10 < k < 22

2011-02-10 22:16:11 補充：
加插多一句:

For a curve y = 3x^2 + (2 +k)x + 3k - 18, it is opening upward and therefore, in case if the equation 3x^2 + (2 +k)x + 3k - 18 = 0 has no real roots, we can ensure that 3x^2 + (2 +k)x + 3k - 18 > 0 for all real values of x.

你所用的方法並不嚴謹
discriminant < 0
跟住solve inequality
done~
雖然答案有比到你,
但係你有沒有諗過10<22 可能會同range of y (y > 18) 有contradiction?

2011-02-10 22:12:07 補充：
10 < k < 22 不是 10 < 22 :P