Answer:
k = 3.
Step-by-step explanation:
If the 2 roots are A and B we have the relations:
AB = 8/k and A+B = -14/k.
We are given that A = 6B so
6B^2 = 8/k
B^2 = 8/6k = 4/3k
B = 2 /√(3k) ......(1)
Now A + B = -14/k so
6B + B = 7B = -14/k
B = -2/k..........(2)
Eliminating B from equations (1) and (2):
2 /√(3k) = -2/k
Cross multiply:
2k = -2√(3k)
Squaring both sides:
4k^2 = 4 * 3k
4k^2 = 12k
k^2 = 3k
k = 3.
