A question

May I use m and n instead of lαl = lβl? It's easy to type!
As the question mentioned, there are two cases to consider:
----------------------------------------------------------
Case 1: m = n
If m=n, it means the equation has equal roots...
Thus discriminant = 0
b^2 - 4ac = 0
(k)^2 - 4(1)(-k + 3) = 0
k^2 + 4k - 12 = 0
(k+6)(k-2) = 0
k=-6 or k=2

Therefore in this case, k=-6 or k=2
----------------------------------------------------------
Case 2: m = -n
If m=-n, it means the equation has 3 real roots ==> Discriminant > 0
However, we won't use the discriminant because by this we only can find the range of k but not the values...
Thus, use SUM OF ROOTS instead...
Sum of roots = -b/a
==> m+(-m) = -k
==> 0 = -k
==> k=0

Therefore in this case, k=0

2007-09-27 14:29:21 補充：
Typing mistake...In case 2, not 3 rootsis 2 roots

= k^2-4(1)(-(k-3)=0
k^2+4k-12=0
k=-6 or k=2

2007-09-26 16:53:33 補充：
因為lαl = lβl ,即是得一個real root so.discriminant = 0Δ = b^2 − 4ac =k^2-4(1)(-(k-3)=0