Quadratic Equationfactormethod

1)
Integral roots 意思是整數根。Not agree.
Let α , β be roots of x² - 5x + m = 0 , then α + β = 5 , α β = m.
Set α = 1 , β = 4 , then m = α β = (1)(4) = 4 , so x² - 5x + 4 = 0 also has integral roots.
2)Let α , β be 2 integral roots of x² + kx + 24 = 0 ,
product of roots = α β = 24 ,
If α = ±1 , β = ±24 , k = α + β = ±25
If α = ± 2 , β = ±12 , k = α + β = ±14
If α =±3 , β = ±8 , k = α + β = ±11
If α =±4 , β = ±6 , k = α + β = ±10
All possible values of k are - 10 , 10 , - 11 , 11 , - 14 , 14 , -25 and 25.

2014-08-21 05:08:15 補充：
k = α + β 應是 - k = α + β , 答案没影響。

no.1 not too understand

Both questions have the same condition, that is, the two roots are integers.