Quadratic Equation

As both roots of the equation are real and positive,
so the sum of roots and product of roots are greater than zero, that is :
-k > 0 and (k + 15) > 0
==> k < 0 and k > -15
==> -15 < k < 0

As k is an integer, therefore, the possible values of k are :
-14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2 and -1.

2014-01-09 14:10:03 補充：
Soory, I miss a condition, Δ should greater than or equal to zero, so
k^2 - 4(k + 15) >= 0
==> k^2 - 4k - 60 >= 0
==> (k + 6)(k - 10) >= 0
==> k <= -6 or k >= 10
Together with -15 < k < 0, we get, -15 < k <= -6
The possible values of k are -14, -13, -12, -11, -10, -9, -8, -7 and -6

k is smaller than 6 or larger than 2*sqrt (41) +2

Explanation:

You know how to take the delta, and k then should be smaller than -6, or larger than 10,

the other part of the solution is -b/2a, so if b is negative, the delta is positve, the solution is positive.

If k is larger than 10, -k/2 is smaller than -5, and then solving the equation delta/4>=25, we get k is larger than 2*sqrt (41)+2, and this answer is larger than 10.

2014-01-12 20:56:12 補充：
Sorry, k is also need to be less than -12, it is because if k is smaller than -6, and then solving the equation delta/4<=9, we get k is smaller than -12.

2014-01-12 21:01:52 補充：
If k is larger than 10, -k/2 is <=-5, and then sqrt(delta)/2 should be >= 5, and then square both sides, we can get the equation.
Also, similarly, if k is smaller than -6, -k/2 is >=3, and then sqrt(delta)/2 should be <=3, and then square both sides, we can get the equation.

D=k^2-60-4k
As the roots of the equation are real,
k^2-60-4k>=0
Since both roots of the equation are positive,
-k>0
k<0

Therefore,
k^2-4k-60>=0 and k<0
(k-10)(k+6)>=0 and k<0
k<=-6 or k>=10 and k<0
Hence the range of k is k<=--6

delta = k^2 - 4(1)(k + 15)
=k^2 - 4k -60
=(k - 10)(k + 6)

coz roots of the equation are real,
(k - 10)(k + 6) > 0
k < -6 or k > 10

but the roots are both real,
the product of roots must be positive(k + 15) ..........product of roots= c / a
so (k + 15) > 0, k > -15

the answer is -15 < k < -6 or k > 10