a . maths (f.4)

I believe that the question should be x^2 + 2(k - 1)x + (5k - 9) = 0
First, the two roots are real and distinct. Thus discriminant > 0
[2(k - 1)]^2 - 4(5k - 9) > 0
4(k^2 - 2k + 1) - 20k + 36 > 0
4k^2 - 8k + 4 - 20k + 36 > 0
4k^2 - 28k + 40 > 0
4(k^2 - 7k + 10) > 0
(k - 2)(k - 5) > 0
k > 5 or k < 2..............(1)
Also the product of the roots must be negative. Thus
(5k - 9) / 1 < 0
5k - 9 < 0
5k < 9
k < 1.8.....................(2)
Combining (1) AND (2), we have k < 1.8